Given a large graph, how to generate a compact summary graph that is configurable by the user and supports multiple graph queries with either no loss or with high accuracy ? The ever growing size of graph datasets makes the above question on graph summarization very pertinent. Although there are several approaches, there does not exist a configurable graph summarization method that offers high compression along with support for multiple graph queries on the summary graph with high accuracy, and allows the user to configure the summarization based on: (1) lossless or lossy summarization, (2) amount of tolerable neighborhood loss, (3) the type of loss it can tolerate, in terms of false-positive edges (i.e., extra edges), false-negative edges (i.e., missing edges), or neither, in both the (a) reconstructed graph and the (b) query answers. To overcome these limitations, we propose a novel graph summarization framework CGS ( Configurable Graph Summarizer ) that builds upon the idea of aggregating nodes with common neighborhoods . The CGS framework consists of three summarization variants, CGS-E , CGS-I, and CGS-U . While CGS-E is a lossless scheme, CGS-I and CGS-U are lossy schemes that allow reconstruction of the input graph with no false-positive edges and no false-negative edges, respectively. To bound the graph reconstruction loss, we introduce a user-specified parameter neighborhood loss tolerance threshold that limits the maximum loss allowed in the neighborhood of each node. This allows graph reconstruction and neighborhood query evaluation with either no loss or with bounded loss guarantees . This, in turn, enables retrieval of multiple graph queries such as shortest path and reachability queries with either no loss or with fairly high accuracy. Empirical evaluation on several synthetic and real-world graphs shows that CGS offers superior summarization than the state-of-the-art methods, and can answer graph queries with fairly high accuracy and efficiency. The implementation code and the datasets are available at https://github.com/sonaelzasimon/CGS_Configurable_Graph_Summarization .

Facility location problems aim to identify the best locations to set up new services. The majority of the existing works typically assume that the users are static. However, there exists a wide array of services such as fuel stations, ATMs, food joints, etc., that are widely accessed by mobile users besides the static ones. Such trajectory-aware services should, therefore, factor in the trajectories of its users rather than simply their static locations. In this work, we introduce the problem of optimal placement of facility locations for such trajectory-aware services that minimize the user inconvenience. The inconvenience of a user is the extra distance traveled by her from her regular path to avail a service. We call this the TIPS problem (Trajectory-aware Inconvenience-minimizing Placement of Services) and consider two variants of it. The goal of the first variant, MAX-TIPS, is to minimize the maximum inconvenience faced by any user, while that of the second, AVG-TIPS, is to minimize the average inconvenience over all the users. We show that both these problems are NP-hard, and propose multiple efficient heuristics to solve them. Empirical evaluation on real urban-scale road networks validate the efficiency and effectiveness of the proposed heuristics.

Optimal location queries identify the best locations to set up new facilities for providing service to its users. For several businesses such as fuel stations, cellphone base-stations, etc., placement queries require taking into account the mobility patterns (or trajectories) of the users. In this work, we formulate the TOPS (Trajectory-Aware Optimal Placement of Services) query that locates the best k sites on a road network for the prevailing user trajectories. The problem is NP-hard. The greedy approach, which is the state-of-the-art technique for this problem, is not scalable and practical for real urban-scale scenarios, primarily due to its high memory footprint beyond the capabilities of commodity machines. To overcome these challenges, we develop an indexing framework called NETCLUS that derives its power through an unique combination of FM sketches with network clustering. Empirical studies show that NETCLUS requires less than 100 s to answer the TOPS query on real datasets comprising of more than 250,000 sites and 120,000 trajectories.

We handle the problem of efficient user-mobility driven macro-cell planning in cellular networks. As cellular networks embrace heterogeneous technologies (including long range 3G/4G and short range WiFi, Femto-cells, etc.), most traffic generated by static users gets absorbed by the short-range technologies, thereby increasingly leaving mobile user traffic to macro-cells. To this end, we consider a novel approach that factors in the trajectories of mobile users as well as the impact of city geographies and their associated road networks for macro-cell planning. Given a budget k of base-stations that can be upgraded, our approach selects a deployment that improves the most number of user trajectories. The generic formulation incorporates the notion of quality of service of a user trajectory as a parameter to allow different application-specific requirements, and operator choices. We show that the proposed trajectory utility maximization problem is NP-hard, and design multiple heuristics. We evaluate our algorithms with real and synthetic datasets emulating different city geographies to demonstrate their efficacy. For instance, with an upgrade budget k of 20%, our algorithms perform 3-8 times better in improving the user quality of service on trajectories when compared to greedy location-based base-station upgrades.

We consider lifetime quality-of-experience (QoE) management for video-on-demand (VoD) users in WiMAX networks. For efficient resource utilization while enhancing user experience, we propose run-time load balancing through joint scheduling among multiple base stations (BSs), referred to as macro scheduling. Macro scheduling employs a utility-maximization approach. To achieve long-term proportional fairness (PF) and manage lifetime QoE, user and flow utilities are modeled as functions of their past service rates, in addition to current channel conditions and bandwidth needs. We show that scheduling flows across multiple BSs jointly to achieve PF is NP-hard in the strong sense. Since approximation algorithms proposed in prior work are computationally expensive for online use, we design efficient heuristics that perform as well as the approximation algorithms. A simulation-based evaluation shows that our overall macro scheduling scheme can improve the number of satisfied users by up to 35% in comparison to other approaches, while only minimally sacrificing on throughput.