Optimizing asset exchanges on blockchain-driven platforms poses a novel and challenging graph query optimization problem. In this model, assets represent vertices and exchanges form edges, recasting the graph query task as a routing problem over a large-scale, dynamic graph. However, the existing solutions fail to solve the problem efficiently due to the non-linear nature of the edge weights defined by a concave swap function. To address the challenge, we propose PRIME, a two-stage iterative graph algorithm designed for the Token Graph Routing Problem (TGRP). The first stage employs a pruned graph search to efficiently identify a set of high-potential routing paths. The second stage formulates the allocation task as a strongly convex optimization problem, which we solve using our novel Adaptive Sign Gradient Method (ASGM) with a linear convergence rate. Extensive experiments on real-world Ethereum data confirm PRIME's advantages over industry baselines. PRIME consistently outperforms the widely-used Uniswap routing algorithm, achieving up to 8.42 basis points (bps) better execution prices on large trades while reducing computation up to 96.7%. The practicality of PRIME is further validated by its deployment in hedge fund production environments, demonstrating its viability as a scalable graph query processing solution for high-frequency decentralized markets.

Graph-based models are a powerful technique for recommendation systems, which seek to leverage the graph structure created by user-item interactions for elevated performance. The majority of them are designed for unsigned graphs, which fail to exploit negative interactions (e.g., dislikes, returns) from users, and hence, incur compromised effectiveness. To tap into such negative signals, in recent years, a number of efforts have been invested towards extending graph neural networks (GNNs) and Transformer models to signed graphs. Unfortunately, the former approaches produce sub-par results due to the lack of access to global information, whereas the latter achieve superior performance for recommendation but suffer from severe over-globalizing problems and substantial computational overhead. To bridge this gap, this paper presents SPGNN, which significantly unleashes the capabilities of GNNs and advances its performance for top-K recommendation in signed graphs through two non-trivial technical contributions. Firstly, we propose to upgrade the neighborhood aggregation scheme in GNNs with two novel notions of signed local proximity (SLP) and signed global proximity (SGP) based on weak balance theory, which can accurately capture sign-aware multi-scale relations between nodes in signed graphs. On top of that, SPGNN includes a theoretically-grounded module for effective feature initialization, which carefully crafts sign-aware structure embeddings via fast spectral decomposition. Extensive experiments show that SPGNN significantly outperforms other unsigned and sign-aware models on six benchmark datasets with up to a gain of 19.42% in Recall and 28.18% in NDCG, which indicates the traditional GNN architecture also holds great potential for signed graph recommendation with appropriate modification. Our code is available at https://github.com/yfsong00/SPGNN.

Influence Maximization (IM) is a crucial problem in social network analysis and has been extensively studied. Traditional approaches rely on designing approximation algorithms using network sampling; however, these methods lack generalizability and depend on an explicit definition of the influence diffusion model as input. Recently, researchers have turned to deep learning methods to address the shortcomings of traditional IM algorithms, but current learning-based IM algorithms still suffer from severe deficiencies in scalability and generalizability. In this paper, we propose IMGNN, a simple, efficient, effective, and generalizable algorithm powered by graph neural networks. IMGNN is a learning-based IM algorithm with strong generalization capability that reduces the overhead of model retraining while also providing fast seed set inference speed. As a result, IMGNN achieves better performance in terms of both efficiency and effectiveness compared to existing IM algorithms. Its exceptional generalization capability also enables it to be trained on small-scale graphs and directly infer the seed node set for large-scale graphs. IMGNN achieves these advantages by adopting a novel design for feature construction and model training, utilizing features constructed from influence propagations over graphs with randomly skipped nodes. This approach enables IMGNN to avoid overfitting to specific network structures while employing a unique technique to improve time efficiency by training on smaller networks. We have conducted extensive experiments using real-world social networks with up to 40 million nodes, and the results strongly demonstrate the superiority of IMGNN in terms of influence spread, seed node set inference speed, and generalizability.

Incomplete node features are ubiquitous in real-world scenarios such as user profiling and cold-start recommendation, which severely hinders the practical deployment of graph learning systems (e.g., GNNs). Existing solutions typically rely on diffusion-based structural smoothing (e.g., feature propagation) to impute missing values. However, we find that these approaches suffer from structural overfitting, leading to three progressive challenges: 1) performance degradation on disjoint graphs, 2) loss of semantic diversity due to over-smoothing, and 3) feature distribution shift when generalizing to unseen graph structures (inductive tasks). To address these challenges, we introduce the DART framework. It begins by employing Global Structural Augmentation (GSA), which establishes global correlations to bridge disjoint components and extend diffusion coverage. Building upon this, we design a semantic rectifier based on masked autoencoding. This module learns the latent feature manifold to recover natural semantic details. Crucially, we introduce a test-time distribution rectification mechanism that projects structurally biased features back onto the learned manifold during inference, effectively bridging the inductive distribution gap. Furthermore, considering that synthetic masking fails to reflect realworld sparsity, we present a new dataset Sailing collected from voyage records with naturally missing attributes. Extensive experiments on six public datasets and Sailing demonstrate that DART significantly outperforms state-of-the-art methods in both transductive and inductive settings. Our code and dataset are available at https://github.com/yfsong00/DART.

Given a social network$G=(V, E)$, the unconstrained profit maximization problem aims to identify a subset$S \subseteq V$that maximizes the net profit, defined as the expected influence spread$\Gamma (S)$of set$S$minus the associated cost$c(S)$, i.e.,$\Gamma (S) - c(S)$. However, this problem presupposes an unlimited budget, which is often impractical in real scenarios. Motivated by this, we investigate the budgeted profit maximization (BPM) problem by adding a budget constraint. Unfortunately, addressing the BPM problem with a theoretical approximation guarantee remains relatively under-explored in the literature. In response, assuming$\Gamma (S)$is known for any$S \subseteq V$, we propose an algorithm that guarantees returning a set$S^{o}$such that$\Gamma (S^{o}) - c(S^{o}) \geq (1 - \frac{1}{e}) \frac{\Gamma (S^*)}{2} - \frac{c(S^*)}{2}$, where$S^*$denotes an optimal solution for BPM. Then, we develop a practical solution, which uses the reverse reachable set (RR-set) technique for influence estimation, without assuming knowledge of$\Gamma (S)$, while still maintaining a strong approximation guarantee. Additionally, similar to existing RR-set-based solutions for influence cascade-related problems, our RR-set-based solution relies on generating a large number of random RR-sets to accurately estimate$\Gamma (S)$. However, the existing RR-set generation method suffers from high memory stall rates due to its irregular memory access patterns, leaving room for further efficiency improvement. Therefore, we propose a new RR-set generation method that utilizes batch execution and cache prefetching. When a memory access is required, instead of stalling while waiting for data, the CPU first issues an asynchronous prefetch request to load the target data into the cache, and then switches to processing the generation of other RR-sets within the same batch, effectively hiding memory access latency. This method can be seamlessly integrated into existing RR-set-based solutions to improve their efficiency. Finally, we conduct extensive experiments on real, large-scale datasets to demonstrate the effectiveness and efficiency of our proposed solutions.

Maritime trajectory modeling is crucial for ensuring the safety and efficiency of maritime transportation. However, the unique challenges of the open ocean-such as the lack of a pre-determined road network and infrequent vessel interactions-render traditional land-based route prediction systems inadequate. To overcome these obstacles, we present ST-Shape, a spatio-temporal trajectory indexing method designed to swiftly retrieve pertinent historical maritime trajectories, thereby facilitating long-term trajectory prediction. ST-Shape approximates trajectories using two-dimensional polygons and constructs the index with shape indices, thus preserving the spatio-temporal properties of each trajectory. Concurrently, we introduce a straightforward yet robust model that harnesses this indexed data to predict vessel movements. To underpin our research, we have curated a comprehensive maritime trajectory dataset from the Atlantic and Pacific Oceans, classified according to diverse navigational scenarios. Our endeavor serves as a foundational step towards expedited spatio-temporal trajectory retrieval for maritime trajectory prediction, marking a significant stride in enhancing maritime safety and navigational efficiency.

The rise of link recommendation systems in online social networks has sparked significant research interest in strategically adding links to enhance social influence. This paper delves into the influence maximization with augmentation (IMA) problem that aims to add k edges connecting seed nodes and ordinary nodes to boost the influence propagation of the given seed set. IMA is a monotone submodular maximization problem so that the greedy algorithm provides a (1-1/e-ε)-approximate solution, where ε is an error term caused by the intractable nature of influence spread computation. Previous work often utilizes an unbiased estimator that relies on the chosen edges for influence estimation, resulting in non-submodular estimate with respect to edge selection. To ensure the overall error being bounded by ε, such an estimator requires Θ(ε/k) multiplicative error for each estimation, incurring prohibitive overhead. Meanwhile, some other work approximates IMA via conventional influence maximization (IM) on an augmented graph by adding a new node for every edge candidate, leading to heavy extra sampling due to a significant increase in graph size. To address these challenges, we design a novel unbiased estimator on the original graph that is independent of the chosen edges by leveraging the tractability of one-hop influence computation. We show that the estimate via our estimator is submodular so that it enables the estimate of all k edges in a whole with a bounded estimation error of Θ(ε), saving O(k2) time compared to the chosen-edge-dependent estimator while retaining the same graph size. Moreover, we propose several techniques based on the properties of our estimator to further speed up the greedy selection. Putting it together, we develop a scalable algorithm for the IMA problem, namely ScaLIM. Finally, extensive experiments are conducted to validate the effectiveness and efficiency of our proposed approach, e.g., ScaLIM is faster than baselines by nearly two orders of magnitude.

Representative subset selection from data streams is a critical problem with wide-ranging applications in web data mining and machine learning, such as social media marketing, big data summarization, and recommendation systems. This problem is often framed as maximizing a monotone submodular function subject to a knapsack constraint, where each data element in the stream has an associated cost, and the goal is to select elements within a budget B to maximize revenue. However, existing algorithms typically rely on restrictive assumptions about the costs of data elements, and their performance bounds heavily depend on the budget B. As a result, these algorithms are only effective in limited scenarios and have super-linear time complexity, making them unsuitable for large-scale data streams. In this paper, we introduce the first linear-time streaming algorithms for this problem, without any assumptions on the data stream, while also minimizing memory usage. Specifically, our single-pass streaming algorithm achieves an approximation ratio of 1/8-ε under O (n) time complexity and O(k log 1/ε) space complexity, where k is the largest cardinality of any feasible solution. Our multi-pass streaming algorithm improves this to a (1/2-ε)-approximation using only three passes over the stream, with O (n/ε log 1/ε) time complexity and O(k/ε log 1/ε) space complexity. Extensive experiments across various applications related to web data mining and social media marketing demonstrate the superiority of our algorithms in terms of both effectiveness and efficiency.

Ethereum, as a representative of Web3, adopts a novel framework called Proposer Builder Separation (PBS) to prevent the centralization of block profits in the hands of institutional Ethereum stakers. Introducing builders to generate blocks based on public transactions, PBS aims to ensure that block profits are distributed among all stakers. Through the auction among builders, only one will win the block in each slot. Ideally, the equilibrium strategy of builders under public information would lead them to bid all block profits. However, builders are now capable of extracting profits from private order flows. In this paper, we explore the effect of PBS with private order flows. Specifically, we propose the asymmetry auction model of MEV-Boost auction. Moreover, we conduct empirical study on Ethereum blocks from January 2023 to May 2024. Our analysis indicates that private order flows contribute to 54.59% of the block value, indicating that different builders will build blocks with different valuations. Interestingly, we find that builders with more private order flows (i.e., higher block valuations) are more likely to win the block, while retain larger proportion of profits. In return, such builders will further attract more private order flows, resulting in a monopolistic market gradually. Our findings reveal that PBS in current stage is unable to balance the profit distribution, which just transits the centralization of block profits from institutional stakers to the monopolistic builder.

Interactive graph search (IGS) has emerged as a powerful paradigm for information retrieval across diverse applications. The goal of IGS is to identify the most appropriate (i.e., deepest) node within a hierarchy for an unknown object, typically leveraging human intelligence such as crowdsourcing as the oracle. Existing IGS algorithms usually rely on reachability queries, such as "is the target node reachable from node x ?", and assume that correct answers are always available. However, in practice, answering such queries is challenging due to the requirement for domain-specific knowledge, resulting in frequent errors in the oracle's responses. As a consequence, the reachability-query-based approaches would perform poorly. In this paper, we propose a practical solution to the IGS problem, leveraging the power of large language models (LLMs) to tackle the issue of reachability queries. Specifically, we formally analyze the inherent properties of real-world hierarchies with the notion of ambiguous nodes and overlapping nodes to debunk the difficulty of reachability queries. In addition, we develop a practical oracle based on LLMs that can answer reachability queries on (near) leaf nodes accurately. Building on the LLM oracle, we propose a similarity-based upward search algorithm, namely SuS, to address the IGS problem. We further enhance SuS with layer-wise search and fast initialization techniques. We evaluate SuS on two real-world datasets against four baseline methods, and the experimental results clearly demonstrate the superiority of our solution.

Nearest-neighbor search is a fundamental task in various applications, including retrieval-augmented generation, recommendation systems, and image classification. To cope with large datasets, Approximate Nearest Neighbor Search (ANNS) is widely used to save computational cost while maintaining high accuracy. Existing ANNS algorithms mainly focus on the Euclidean distance. However, in practice, cosine similarity is commonly adopted in downstream tasks. In this paper, we study the Monotonic Relative Neighbor Graph (MRNG), a state-of-the-art graph-based ANNS structure that shows strong performance under Euclidean distance. We analyze MRNG under cosine similarity and prove two key properties: (1) greedy search on the graph always moves closer to the query until the exact nearest neighbor is found, and (2) the graph's maximum out-degree is bounded by a constant independent of the dataset size. These properties lead to fast search and compact index size. However, constructing an exact MRNG is computationally expensive on large datasets. Moreover, existing approximate construction methods tailored for Euclidean distance, e.g., Euclidean centroid or KD-Trees, are not suitable for cosine similarity. To address these issues, we propose an approximate version of MRNG, named Hemi-Sphere Centroids Graph (HSCG), which uses the hemi-sphere centroids as the entry points and employs locality-sensitive hashing to initialize the graph efficiently. Extensive experiments on eight datasets demonstrate the superiority of HSCG in terms of both search performance and index size compared to existing representative algorithms under cosine similarity.

Large language models (LLMs) have garnered unprecedented advancements across diverse fields, ranging from natural language processing to computer vision and beyond. The prowess of LLMs is underpinned by their substantial model size, extensive and diverse datasets, and the vast computational power harnessed during training, all of which contribute to the emergent abilities of LLMs (e.g., in-context learning) that are not present in small models. Within this context, the mixture of experts (MoE) has emerged as an effective method for substantially scaling up model capacity with minimal computation overhead, gaining significant attention from academia and industry. Despite its growing prevalence, there lacks a systematic and comprehensive review of the literature on MoE. This survey seeks to bridge that gap, serving as an essential resource for researchers delving into the intricacies of MoE. We first briefly introduce the structure of the MoE layer, followed by proposing a new taxonomy of MoE. Next, we overview the core designs for various MoE models including both algorithmic and systemic aspects, alongside collections of available open-source implementations, hyperparameter configurations and empirical evaluations. Furthermore, we delineate the multifaceted applications of MoE in practice, and outline some potential directions for future research.

Link recommendation systems in online social networks (OSNs), such as Facebook's "People You May Know", Twitter's "Who to Follow", and Instagram's "Suggested Accounts", facilitate the formation of new connections among users. This paper addresses the challenge of link recommendation for the purpose of social influence maximization. In particular, given a graph G and the seed set S, our objective is to select k edges that connect seed nodes and ordinary nodes to optimize the influence dissemination of the seed set. This problem, referred to as influence maximization with augmentation (IMA), has been proven to be NP-hard.

Graph embedding aims at mapping each node to a low-dimensional vector, beneficial for various applications like pattern matching, retrieval augmented generation and recommendation. In this paper, we study the large-scale temporal graph embedding problem. Different from simple graphs, each edge has a timestamp in temporal graphs, which requires the embeddings to encode the temporal biases. Factorizing similarity matrix is a common approach for generating simple graph embeddings where similarity can be well characterized by some conventional metrics like personalized PageRank. However, how to construct a similarity that can encode interactions with temporal biases is a critical problem for large scale temporal graphs. To address this, we introduce the concept of temporal-based bipartite graph (TBG) and develop the temporal preferential attachment similarity (TPASim) that reflects concurrent node activity over time. Directly factorizing the TPASim matrix, which contains nearly n 2 non-zeros, is not feasible for large graphs with n nodes. Instead, we present LTGE, which constructs and factorizes a temporal matrix with at most 2 m non-zeros, where m is the number of edges. Our theoretical analysis shows that LTGE achieves the same embeddings as factorizing the TPASim matrix but significantly reduces complexity by a factor of n 2 / m. On the other hand, when graphs evolve over time, to avoid recomputing, we further propose LTGEInc that utilizes a novel incremental singular value decomposition (SVD) algorithm with provable guarantee for updating the embeddings. Extensive experiments on several datasets with up to 17 million nodes and 1.3 billion edges demonstrate that LTGE outperforms the state of the art significantly and is orders of magnitude faster than the baselines specially designed for temporal graphs. For embeddings update, LTGEInc retains the performance with small computational overhead.

We introduce Galaxybase, a native distributed graph database that addresses the increasing demands for processing large volumes of graph data in diverse industries like finance, manufacturing, and government. Designed to handle the requirements of both transactional and analytical workloads, Galaxybase stands out with its novel data storage and transaction mechanisms. At its core, Galaxybase utilizes a Log-Structured Adjacency List coupled with an Edge Page structure, optimizing read-write operations across a spectrum of tasks such as graph traversals and single edge queries. A notable aspect of Galaxybase is its execution of custom distributed transaction modes tailored for HTAP transactions, allowing for the facilitation of bidirectional and interactive transactions. It ensures data integrity and minimal latency while enabling simultaneous processing of OLTP and OLAP workloads without blocking. Experimental results show that Galaxybase achieves high throughput and low latency in both OLTP and OLAP workloads, across various graph query scenarios and resource conditions. Galaxybase has been deployed in leading banks, education, telecommunication and energy sectors in China, consistently maintaining robust performance for HTAP workloads over the years.

Given a graph \mathcalG , the spanning centrality (SC) of an edge e measures the importance of e for \mathcalG to be connected. In practice, SC has seen extensive applications in computational biology, electrical networks, and combinatorial optimization. However, it is highly challenging to compute the SC of all edges (AESC) on large graphs. Existing techniques fail to deal with such graphs, as they either suffer from expensive matrix operations or require sampling numerous long random walks. To circumvent these issues, this paper proposes TGT and its enhanced version TGT+, two algorithms for AESC computation that offers rigorous theoretical approximation guarantees. In particular, TGT remedies the deficiencies of previous solutions by conducting deterministic graph traversals with carefully-crafted truncated lengths. TGT+ further advances TGT in terms of both empirical efficiency and asymptotic performance while retaining result quality, based on the combination of TGT with random walks and several additional heuristic optimizations. We experimentally evaluate TGT+ against recent competitors for AESC using a variety of real datasets. The experimental outcomes authenticate that TGT+ outperforms state of the arts often by over one order of magnitude speedup without degrading the accuracy.

The problem of constrained subset selection from a large data stream for profit maximization has many applications in web data mining and machine learning, such as social advertising, team formation and recommendation systems. Such a problem can be formulated as maximizing a regularized submodular function under certain constraints. In this paper, we consider a generalized k-system constraint, which captures various requirements in real-world applications. For this problem, we propose the first streaming algorithm with provable performance bounds, leveraging a novel multitudinous distorted filter framework. The empirical performance of our algorithm is extensively evaluated in several applications including web data mining and recommendation systems, and the experimental results demonstrate the superiorities of our algorithm in terms of both effectiveness and efficiency.

Graph Neural Networks (GNNs) have shown superior performance for semi-supervised learning of numerous web applications, such as classification on web services and pages, analysis of online social networks, and recommendation in e-commerce. The state of the art derives representations for all nodes in graphs following the same diffusion (message passing) model without discriminating their uniqueness. However, (i) labeled nodes involved in model training usually account for a small portion of graphs in the semi-supervised setting, and (ii) different nodes locate at different graph local contexts and it inevitably degrades the representation qualities if treating them undistinguishedly in diffusion.

A lot of applications in web economics need to maximize the revenue under a budget for payments and also guarantee the truthfulness of users, so Budget-Feasible Mechanism (BFM) Design has aroused great interests during last decade. Most of the existing BFMs concentrate on maximizing a monotone submodular function subject to a knapsack constraint, which is insufficient for many applications with complex objectives or constraints. Observing this, the recent studies (e.g., [4, 5, 11]) have considered non-monotone submodular objectives or more complex constraints such as a k-system constraint. In this study, we follow this line of research and propose truthful BFMs with improved performance bounds for non-monotone submodular objectives with or without a k-system constraint. Our BFMs leverage the idea of providing random prices to users while deferring the decision on the final winning set, and are also based on a novel randomized algorithm for the canonical constrained submodular maximization problem achieving better performance bounds compared to the state-of-the-art. Finally, the effectiveness and efficiency of our approach are demonstrated by extensive experiments on several applications about social network marketing, crowdsourcing and personalized recommendation.

Given an undirected graph G, the effective resistance r(s,t) measures the dissimilarity of node pair s,t in G, which finds numerous applications in real-world problems, such as recommender systems, combinatorial optimization, molecular chemistry, and electric power networks. Existing techniques towards pairwise effective resistance estimation either trade approximation guarantees for practical efficiency, or vice versa. In particular, the state-of-the-art solution is based on a multitude of Monte Carlo random walks, rendering it rather inefficient in practice, especially on large graphs. Motivated by this, this paper first presents an improved Monte Carlo approach, AMC, which reduces both the length and amount of random walks required without degrading the theoretical accuracy guarantee, through careful theoretical analysis and an adaptive sampling scheme. Further, we develop a greedy approach, GEER, which combines AMC with sparse matrix-vector multiplications in an optimized and non-trivial way. GEER offers significantly improved practical efficiency over AMC without compromising its asymptotic performance and accuracy guarantees. Extensive experiments on multiple benchmark datasets reveal that GEER is orders of magnitude faster than the state of the art in terms of computational time when achieving the same accuracy.

With rapidly growing sizes of online social networks, computational challenges arise in analyzing the diffusion process over networks. Sampling methods are commonly used to study the cascade effect and estimate users' influence. In this paper, we propose a brand-new sampling method, called 2-hop+ sampling for quickly and accurately estimating the cascade size generated by a set of seed users under the independent cascade model. Our method generates only samples with at least one 2-hop live path from the source to reduce the number of samples. We further enhance the sampling efficiency of our method by a SkipEdge technique. Moreover, we improve the generalized stopping rule algorithm to obtain an (,)-estimate of the mean of random variables with fewer samples needed. Extensive experiments with real-world datasets show that our techniques can significantly improve the estimation efficiency compared to the state-of-the-art methods.

Interactive graph search (IGS) uses human intelligence to locate the target node in hierarchy, which can be applied for image classification, product categorization and searching a database. Specifically, IGS aims to categorize an object from a given category hierarchy via several rounds of interactive queries. In each round of query, the search algorithm picks a category and receives a boolean answer on whether the object is under the chosen category. The main efficiency goal asks for the minimum number of queries to identify the correct hierarchical category for the object. In this paper, we study the average-case interactive graph search (AIGS) problem that aims to minimize the expected number of queries when the objects follow a probability distribution. We propose a greedy search policy that splits the candidate categories as evenly as possible with respect to the probability weights, which offers an approximation guarantee of$O(\log n)$for AIGS given the category hierarchy is a directed acyclic graph (DAG), where$n$is the total number of categories. Meanwhile, if the input hierarchy is a tree, we show that a constant approximation factor of$(1+\sqrt{5})/2$can be achieved. Furthermore, we present efficient implementations of the greedy policy, namely GreedyTree and GreedyDAG, that can quickly categorize the object in practice. Extensive experiments in real-world scenarios are carried out to demonstrate the superiority of our proposed methods.

Thanks to billions of users in online social networks (OSNs), viral marketing becomes one of the most effective promotion channels for various new products or campaigns. Influence maximization is a classic problem in viral marketing, which has been extensively studied in the past two decades. Existing algorithms for influence maximization, however, mostly focus on single machine processing. To address the influence maximization problem on a massive scale, we design distributed algorithms via a cluster of machines, which can effectively speed up the computation while maintaining the state-of-the-art (1 -1/e-c)-approximation guarantee. Our distributed algorithms consist of two building blocks: (i) distributed reverse influence sampling, and (ii) element-distributed maximum coverage. We carry out extensive experiments on real datasets with millions of nodes and billions of edges to demonstrate the scalability of our distributed algorithms for both influence maximization and maximum coverage. In particular, our distributed algorithms accelerate the state-of-the-art IMM algorithm by 31x-56x times using a machine with 64 cores.

The interactive graph search (IGS) problem aims to locate an initially unknown target node leveraging human intelligence. In IGS, we can gradually find the target node by sequentially asking humans some reachability queries like "is the target node reachable from a given node x?". However, human workers may make mistakes when answering these queries. Motivated by this concern, in this paper, we study a noisy version of the IGS problem. Our objective in this problem is to minimize the query complexity while ensuring accuracy. We propose a method to select the query node such that we can push the search process as much as possible and an online method to infer which node is the target after collecting a new answer. By rigorous theoretical analysis, we show that the query complexity of our approach is near-optimal up to a constant factor. The extensive experiments on two real datasets also demonstrate the superiorities of our approach.

Given a social network G with n nodes and m edges, a positive integer k , and a cascade model C , the influence maximization (IM) problem asks for k nodes in G such that the expected number of nodes influenced by the k nodes under cascade model C is maximized. The state-of-the-art approximate solutions run in O(k(n+m) log n/ ε 2 ) expected time while returning a (1 - 1/ e - ε) approximate solution with at least 1 - 1/ n probability. A key phase of these IM algorithms is the random reverse reachable (RR) set generation, and this phase significantly affects the efficiency and scalability of the state-of-the-art IM algorithms. In this article, we present a study on this key phase and propose an efficient random RR set generation algorithm under IC model. With the new algorithm, we show that the expected running time of existing IM algorithms under IC model can be improved to O(k ċ n log n ċ 2 ), when for any node v , the total weight of its incoming edges is no larger than a constant. For the general IC model where the weights are skewed, we present a sampling algorithm SKIP. To the best of our knowledge, it is the first index-free algorithm that achieves the optimal time complexity of the sorted subset sampling problem. Moreover, existing approximate IM algorithms suffer from scalability issues in high influence networks where the size of random RR sets is usually quite large. We tackle this challenging issue by reducing the average size of random RR sets without sacrificing the approximation guarantee. The proposed solution is orders of magnitude faster than states of the art as shown in our experiment. Besides, we investigate the issues of forward propagation and derive its time complexity with our proposed subset sampling techniques. We also present a heuristic condition to indicate when the forward propagation approach should be utilized to estimate the expected influence of a given seed set.

We consider the revenue maximization problem in social advertising, where a social network platform owner needs to select seed users for a group of advertisers, each with a payment budget, such that the total expected revenue that the owner gains from the advertisers by propagating their ads in the network is maximized. Previous studies on this problem show that it is intractable and present approximation algorithms. We revisit this problem from a fresh perspective and develop novel efficient approximation algorithms, both under the setting where an exact influence oracle is assumed and under one where this assumption is relaxed. Our approximation ratios significantly improve upon the previous ones. Furthermore, we empirically show, using extensive experiments on four datasets, that our algorithms considerably outperform the existing methods on both the solution quality and computation efficiency.

Proof-of-Work (PoW) is the most widely adopted incentive model in current blockchain systems, which unfortunately is energy inefficient. Proof-of-Stake (PoS) is then proposed to tackle the energy issue. The rich-get-richer concern of PoS has been heavily debated in the blockchain community. The debate is centered around the argument that whether rich miners possessing more stakes will obtain higher staking rewards and further increase their potential income in the future. In this paper, we define two types of fairness, i.e., expectational fairness and robust fairness, that are useful for answering this question. In particular, expectational fairness illustrates that the expected income of a miner is proportional to her initial investment, indicating that the expected return on investment is a constant. To better capture the uncertainty of mining outcomes, robust fairness is proposed to characterize whether the return on investment concentrates to a constant with high probability as time evolves. Our analysis shows that the classical PoW mechanism can always preserve both types of fairness as long as the mining game runs for a sufficiently long time. Furthermore, we observe that current PoS blockchains implement various incentive models and discuss three representatives, namely ML-PoS, SL-PoS and C-PoS. We find that (i) ML-PoS (e.g., Qtum and Blackcoin) preserves expectational fairness but may not achieve robust fairness, (ii) SL-PoS (e.g., NXT) does not protect any type of fairness, and (iii) C-PoS (e.g., Ethereum 2.0) outperforms ML-PoS in terms of robust fairness while still maintaining expectational fairness. Finally, massive experiments on real blockchain systems and extensive numerical simulations are performed to validate our analysis.

Online Social Network (OSN) providers usually conduct advertising campaigns by inserting social ads into promoted posts. Whenever a user engages in a promoted ad, she may further propagate the promoted ad to her followers recursively and the propagation process is known as the word-of-mouth effect. In order to spread the promotion cascade widely and efficiently, the OSN provider often tends to select the influencers, who normally have large audiences over the social network, to initiate the advertising campaign. This marketing model, also termed as influencer marketing, has been gaining increasing traction and investment and is rapidly becoming one of the most widely-used channels in digital marketing. In this paper, we formulate the problem for the OSN provider to derive the influence contributions of influencers given the campaign result, considering the viral propagation of the ads, namely influence contribution allocation (ICA) . We make a connection between ICA and the concept of Shapley value in cooperative game theory to reveal the rationale behind ICA. A naive method to obtain the solution to ICA is to enumerate all possible cascades delivering the campaign result, resulting in an exponential number of potential cascades, which is computationally intractable. Moreover, generating a cascade producing the exact campaign result is non-trivial. Facing the challenges, we develop an exact solution in linear time under the linear threshold (LT) model, and devise a fully polynomial-time randomized approximation scheme (FPRAS) under the independent cascade (IC) model. Specifically, under the IC model, we propose an efficient approach to estimate the expected influence contribution in probabilistic graphs modeling OSNs by designing a scalable sampling method with provable accuracy guarantees. We conduct extensive experiments and show that our algorithms yield solutions with remarkably higher quality over several baselines and improve the sampling efficiency significantly.

Given a social network G, the profit maximization (PM) problem asks for a set of seed nodes to maximize the profit, i.e., revenue of influence spread less the cost of seed selection. The target profit maximization (TPM) problem, which generalizes the PM problem, aims to select a subset of seed nodes from a target user set T to maximize the profit. Existing algorithms for PM mostly consider the nonadaptive setting, where all seed nodes are selected in one batch without any knowledge on how they may influence other users. In this paper, we study TPM in adaptive setting, where the seed users are selected through multiple batches, such that the selection of a batch exploits the knowledge of actual influence in the previous batches. To acquire an overall understanding, we study the adaptive TPM problem under both the oracle model and the noise model, and propose ADG and AddATP algorithms to address them with strong theoretical guarantees, respectively. In addition, to better handle the sampling errors under the noise model, we propose the idea of hybrid error based on which we design a novel algorithm HATP that boosts the efficiency of AddATP significantly. We conduct extensive experiments on real social networks to evaluate the performance, and the experimental results strongly confirm the superiorities and effectiveness of our solutions.

Influential nodes with rich connections in online social networks (OSNs) are of great values to initiate marketing campaigns. However, the potential influence spread that can be generated by these influential nodes is hidden behind the structures of OSNs, which are often held by OSN providers and unavailable to advertisers for privacy concerns. A social advertising model known as influencer marketing is to have OSN providers offer and price candidate nodes for advertisers to purchase for seeding marketing campaigns. In this setting, a reasonable price profile for the candidate nodes should effectively reflect the expected influence gain they can bring in a marketing campaign. In this paper, we study the problem of pricing the influential nodes based on their expected influence spread to help advertisers select the initiators of marketing campaigns without the knowledge of OSN structures. We design a function characterizing the divergence between the price and the expected influence of the initiator sets. We formulate the problem to minimize the divergence and derive an optimal price profile. An advanced algorithm is developed to estimate the price profile with accuracy guarantees. Experiments with real OSN datasets show that our pricing algorithm can significantly outperform other baselines.

As a dual problem of influence maximization, the seed minimization problem asks for the minimum number of seed nodes to influence a required number η of users in a given social network G. Existing algorithms for seed minimization mostly consider the non-adaptive setting, where all seed nodes are selected in one batch without observing how they may influence other users. In this paper, we study seed minimization in the adaptive setting, where the seed nodes are selected in several batches, such that the choice of a batch may exploit information about the actual influence of the previous batches. We propose a novel algorithm, ASTI, which addresses the adaptive seed minimization problem in $O\Big(\fracη \cdot (m+n) \varepsilon^2 łn n \Big)$ expected time and offers an approximation guarantee of $\frac(łn η+1)^2 (1 - (1-1/b)^b) (1-1/e)(1-\varepsilon) $ in expectation, where η is the targeted number of influenced nodes, b is size of each seed node batch, and $\varepsilon \in (0, 1)$ is a user-specified parameter. To the best of our knowledge, ASTI is the first algorithm that provides such an approximation guarantee without incurring prohibitive computation overhead. With extensive experiments on a variety of datasets, we demonstrate the effectiveness and efficiency of ASTI over competing methods.

We consider the edge uncertainty in an undirected graph and study the k -median (resp. k -center) problems, where the goal is to partition the graph nodes into k clusters such that the average (resp. minimum) connection probability between each node and its cluster's center is maximized. We analyze the hardness of these problems, and propose algorithms that provide considerably improved approximation guarantees than the existing studies do. Specifically, our algorithms offer (1 -- 1/e)-approximations for the k -median problem and (OPTck)-approximations for the k -center problem, where OPTck is the optimal objective function value for k -center. In addition, our algorithms incorporate several non-trivial optimizations that significantly enhance their practical efficiency. Extensive experimental results demonstrate that our algorithms considerably outperform the existing methods on both computation efficiency and the quality of clustering results.

Influence maximization is a classic and extensively studied problem with important applications in viral marketing. Existing algorithms for influence maximization, however, mostly focus on offline processing, in the sense that they do not provide any output to the user until the final answer is derived, and that the user is not allowed to terminate the algorithm early to trade the quality of solution for efficiency. Such lack of interactiveness and flexibility leads to poor user experience, especially when the algorithm incurs long running time.

Given a social network G , the influence maximization (IM) problem seeks a set S of k seed nodes in G to maximize the expected number of nodes activated via an influence cascade starting from S. Although a lot of algorithms have been proposed for IM, most of them only work under the non-adaptive setting, i.e., when all k seed nodes are selected before we observe how they influence other users. In this paper, we study the adaptive IM problem, where we select the k seed nodes in batches of equal size b , such that the choice of the i -th batch can be made after the influence results of the first i - 1 batches are observed. We propose the first practical algorithms for adaptive IM with an approximation guarantee of 1 − exp(ξ − 1) for b = 1 and 1 − exp(ξ − 1 + 1/ e ) for b > 1, where ξ is any number in (0, 1). Our approach is based on a novel AdaptGreedy framework instantiated by non-adaptive IM algorithms, and its performance can be substantially improved if the non-adaptive IM algorithm has a small expected approximation error. However, no current non-adaptive IM algorithms provide such a desired property. Therefore, we further propose a non-adaptive IM algorithm called EPIC, which not only has the same worst-case performance bounds with that of the state-of-the-art non-adaptive IM algorithms, but also has a reduced expected approximation error. We also provide a theoretical analysis to quantify the performance gain brought by instantiating AdaptGreedy using EPIC, compared with a naive approach using the existing IM algorithms. Finally, we use real social networks to evaluate the performance of our approach through extensive experiments, and the experimental experiments strongly corroborate the superiorities of our approach.

Information can be disseminated widely and rapidly through Online Social Networks (OSNs) with “word-of-mouth” effects. Viral marketing is such a typical application in which new products or commercial activities are advertised by some seed users in OSNs to other users in a cascading manner. The selection of initial seed users yields a tradeoff between the expense and reward of viral marketing. In this paper, we define a general profit metric that naturally combines the benefit of influence spread with the cost of seed selection in viral marketing. We carry out a comprehensive study on finding a set of seed nodes to maximize the profit of viral marketing. We show that the profit metric is significantly different from the influence metric in that it is no longer monotone. This characteristic differentiates the profit maximization problem from the traditional influence maximization problem. We develop new seed selection algorithms for profit maximization with strong approximation guarantees. We also derive several upper bounds to benchmark the practical performance of an algorithm on any specific problem instance. Experimental evaluations with real OSN datasets demonstrate the effectiveness of our algorithms and techniques.

Influence Maximization is an extensively-studied problem that targets at selecting a set of initial seed nodes in the Online Social Networks (OSNs) to spread the influence as widely as possible. However, it remains an open challenge to design fast and accurate algorithms to find solutions in large-scale OSNs. Prior Monte-Carlo-simulation-based methods are slow and not scalable, while other heuristic algorithms do not have any theoretical guarantee and they have been shown to produce poor solutions for quite some cases. In this paper, we propose hop-based algorithms that can easily scale to millions of nodes and billions of edges. Unlike previous heuristics, our proposed hop-based approaches can provide certain theoretical guarantees. Experimental evaluations with real OSN datasets demonstrate the efficiency and effectiveness of our algorithms.