Let $\mathcal{F}$ be a family of graphs, and let $p,r$ be nonnegative integers. The \textsc{$(p,r,\mathcal{F})$-Covering} problem asks whether for a graph $G$ and an integer $k$, there exists a set $D$ of at most $k$ vertices in $G$ such that $G^p\setminus N_G^r[D]$ has no induced subgraph isomorphic to a graph in $\mathcal{F}$, where $G^p$ is the $p$-th power of $G$. The \textsc{$(p,r,\mathcal{F})$-Packing} problem asks whether for a graph $G$ and an integer $k$, $G^p$ has $k$ induced subgraphs $H_1,\ldots,H_k$ such that each $H_i$ is isomorphic to a graph in $\mathcal{F}$, and for distinct $i,j\in \{1, \ldots, k\}$, the distance between $V(H_i)$ and $V(H_j)$ in $G$ is larger than $r$. We show that for every fixed nonnegative integers $p,r$ and every fixed nonempty finite family $\mathcal{F}$ of connected graphs, the \textsc{$(p,r,\mathcal{F})$-Covering} problem with $p\leq2r+1$ and the \textsc{$(p,r,\mathcal{F})$-Packing} problem with $p\leq2\lfloor r/2\rfloor+1$ admit almost linear kernels on every nowhere dense class of graphs, and admit linear kernels on every class of graphs with bounded expansion, parameterized by the solution size $k$. We obtain the same kernels for their annotated variants. As corollaries, we prove that \textsc{Distance-$r$ Vertex Cover}, \textsc{Distance-$r$ Matching}, \textsc{$\mathcal{F}$-Free Vertex Deletion}, and \textsc{Induced-$\mathcal{F}$-Packing} for any fixed finite family $\mathcal{F}$ of connected graphs admit almost linear kernels on every nowhere dense class of graphs and linear kernels on every class of graphs with bounded expansion. Our results extend the results for \textsc{Distance-$r$ Dominating Set} by Drange et al. (STACS 2016) and Eickmeyer et al. (ICALP 2017), and the result for \textsc{Distance-$r$ Independent Set} by Pilipczuk and Siebertz (EJC 2021).

RDF data are used to model knowledge in various areas such as life sciences, Semantic Web, bioinformatics, and social graphs. The size of real RDF data reaches billions of triples. This calls for a framework for efficiently processing RDF data. The core function of processing RDF data is subgraph pattern matching. There have been two completely different directions for supporting efficient subgraph pattern matching. One direction is to develop specialized RDF query processing engines exploiting the properties of RDF data for the last decade, while the other direction is to develop efficient subgraph isomorphism algorithms for general, labeled graphs for over 30 years. Although both directions have a similar goal (i.e., finding subgraphs in data graphs for a given query graph), they have been independently researched without clear reason. We argue that a subgraph isomorphism algorithm can be easily modified to handle the graph homomorphism, which is the RDF pattern matching semantics, by just removing the injectivity constraint. In this paper, based on the state-of-the-art subgraph isomorphism algorithm, we propose an in-memory solution, Turbo HOM++ , which is tamed for the RDF processing, and we compare it with the representative RDF processing engines for several RDF benchmarks in a server machine where billions of triples can be loaded in memory. In order to speed up Turbo HOM++ , we also provide a simple yet effective transformation and a series of optimization techniques. Extensive experiments using several RDF benchmarks show that Turbo HOM++ consistently and significantly outperforms the representative RDF engines. Specifically, Turbo HOM++ outperforms its competitors by up to five orders of magnitude.

Graph triangulation, which finds all triangles in a graph, has been actively studied due to its wide range of applications in the network analysis and data mining. With the rapid growth of graph data size, disk-based triangulation methods are in demand but little researched. To handle a large-scale graph which does not fit in memory, we must iteratively load small parts of the graph. In the existing literature, achieving the ideal cost has been considered to be impossible for billion-scale graphs due to the memory size constraint. In this paper, we propose an overlapped and parallel disk-based triangulation framework for billion-scale graphs, OPT, which achieves the ideal cost by (1) full overlap of the CPU and I/O operations and (2) full parallelism of multi-core CPU and FlashSSD I/O. In OPT, triangles in memory are called the internal triangles while triangles constituting vertices in memory and vertices in external memory are called the external triangles. At the macro level, OPT overlaps the internal triangulation and the external triangulation, while it overlaps the CPU and I/O operations at the micro level. Thereby, the cost of OPT is close to the ideal cost. Moreover, OPT instantiates both vertex-iterator and edge-iterator models and benefits from multi-thread parallelism on both types of triangulation. Extensive experiments conducted on large-scale datasets showed that (1) OPT achieved the elapsed time close to that of the ideal method with less than 7% of overhead under the limited memory budget, (2) OPT achieved linear speed-up with an increasing number of CPU cores, (3) OPT outperforms the state-of-the-art parallel method by up to an order of magnitude with 6 CPU cores, and (4) for the first time in the literature, the triangulation results are reported for a billion-vertex scale real-world graph.

As social network services connect people across the world, influence maximization, i.e., finding the most influential nodes (or individuals) in the network, is being actively researched with applications to viral marketing. One crucial challenge in scalable influence maximization processing is evaluating influence, which is #P-hard and thus hard to solve in polynomial time. We propose a scalable influence approximation algorithm, Independent Path Algorithm (IPA) for Independent Cascade (IC) diffusion model. IPA efficiently approximates influence by considering an independent influence path as an influence evaluation unit. IPA are also easily parallelized by simply adding a few lines of OpenMP meta-programming expressions. Also, overhead of maintaining influence paths in memory is relieved by safely throwing away insignificant influence paths. Extensive experiments conducted on large-scale real social networks show that IPA is an order of magnitude faster and uses less memory than the state of the art algorithms. Our experimental results also show that parallel versions of IPA speeds up further as the number of CPU cores increases, and more speed-up is achieved for larger datasets. The algorithms have been implemented in our demo application for influence maximization (available at http://dm.postech.ac.kr/ipa demo), which efficiently finds the most influential nodes in a social network.

Graphs are used to model many real objects such as social networks and web graphs. Many real applications in various fields require efficient and effective management of large-scale graph structured data. Although distributed graph engines such as GBase and Pregel handle billion-scale graphs, the user needs to be skilled at managing and tuning a distributed system in a cluster, which is a nontrivial job for the ordinary user. Furthermore, these distributed systems need many machines in a cluster in order to provide reasonable performance. In order to address this problem, a disk-based parallel graph engine called Graph-Chi, has been recently proposed. Although Graph-Chi significantly outperforms all representative (disk-based) distributed graph engines, we observe that Graph-Chi still has serious performance problems for many important types of graph queries due to 1) limited parallelism and 2) separate steps for I/O processing and CPU processing. In this paper, we propose a general, disk-based graph engine called TurboGraph to process billion-scale graphs very efficiently by using modern hardware on a single PC. TurboGraph is the first truly parallel graph engine that exploits 1) full parallelism including multi-core parallelism and FlashSSD IO parallelism and 2) full overlap of CPU processing and I/O processing as much as possible. Specifically, we propose a novel parallel execution model, called pin-and-slide. TurboGraph also provides engine-level operators such as BFS which are implemented under the pin-and-slide model. Extensive experimental results with large real datasets show that TurboGraph consistently and significantly outperforms Graph-Chi by up to four orders of magnitude! Our implementation of TurboGraph is available at ``http://wshan.net/turbograph}" as executable files.

Influence maximization problem with applications to viral marketing has gained much attention. Underlying influence diffusion models affect influence maximizing nodes because they focus on difference aspect of influence diffusion. Nevertheless, existing diffusion models overlook two important aspects of real-world marketing - continuous trials and time restriction. This paper proposes a new realistic influence diffusion model called Continously activated and Time-restricted IC (CT-IC) model which generalizes the IC model by embedding the above two aspects. We first prove that CT-IC model satisfies two crucial properties - monotonicity and submodularity. We then provide an efficient method for calculating exact influence spread when a social network is restricted to a directed tree and a simple path. Finally, we propose a scalable algorithm for influence maximization under CT-IC model called CT-IPA. Our experiments show that CT-IC model provides seeds of higher influence spread than IC model and CT-IPA is four orders of magnitude faster than the greedy algorithm while providing similar influence spread to the greedy algorithm.

Conventional video search systems, to find relevant videos, rely on textual data such as video titles, annotations, and text around the video. Nowadays, video recording devices such as ameras, smartphones and car blackboxes are equipped with GPS sensors and able to capture videos with spatiotemporal information such as time, location and camera direction. We call such videos georeferenced videos. This paper presents a georeferenced video retrieval system, geosearch, which efficiently retrieves videos containing a certain point or range in the map. To enable a fast search of georeferenced videos, geosearch adopts a novel data structure MBTR (Minimum Bounding Tilted Rectangle) in the leaf nodes of R-Tree. New algorithms are developed to build MBTRs from georeferenced videos and to efficiently process point and range queries on MBTRs. We demonstrate our system on real georeferenced videos, and show that, compared to previous methods, geosearch substantially reduces the index size and also improves the search speed for georeferenced video data. Our online demo is available at "http://dm.hwanjoyu.org/geosearch".

With the advent of multicore processors,it has become imperative to write parallel programs if one wishes to exploit the next generation of processors. This paper deals with skyline computation as a case study of parallelizing database operations on multicore architectures. We compare two parallel skyline algorithms: a parallel version of the branch-and-bound algorithm (BBS) and a new parallel algorithm based on skeletal parallel programming. Experimental results show despite its simple design, the new parallel algorithm is comparable to parallel BBS in speed. For sequential skyline computation, the new algorithm far outperforms sequential BBS when the density of skyline tuples is low.

In efforts to overcome the complexity of the syntax and the lack of formal semantics of conventional hardware description languages, a number of functional hardware description languages have been developed. Like conventional hardware description languages, however, functional hardware description languages eventually convert all source programs into netlists, which describe wire connections in hardware circuits at the lowest level and conceal all high-level descriptions written into source programs.