An Order-based Algorithm for Minimum Dominating Set with Application in Graph Mining

Dominating set is a set of vertices of a graph such that all other vertices have a neighbour in the dominating set. We propose a new order-based randomised local search (RLS$_o$) algorithm to solve minimum dominating set problem in large graphs. Experimental evaluation is presented for multiple types of problem instances. These instances include unit disk graphs, which represent a model of wireless networks, random scale-free networks, as well as samples from two social networks and real-world graphs studied in network science. Our experiments indicate that RLS$_o$ performs better than both a classical greedy approximation algorithm and two metaheuristic algorithms based on ant colony optimisation and local search. The order-based algorithm is able to find small dominating sets for graphs with tens of thousands of vertices. In addition, we propose a multi-start variant of RLS$_o$ that is suitable for solving the minimum weight dominating set problem. The application of RLS$_o$ in graph mining is also briefly demonstrated

The Power Of Locality In Network Algorithms

Over the last decade we have witnessed the rapid proliferation of large-scale complex networks, spanning many social, information and technological domains. While many of the tasks which users of such networks face are essentially global and involve the network as a whole, the size of these networks is huge and the information available to users is only local. In this dissertation we show that even when faced with stringent locality constraints, one can still effectively solve prominent algorithmic problems on such networks. In the first part of the dissertation we present a natural algorithmic framework designed to model the behaviour of an external agent trying to solve a network optimization problem with limited access to the network data. Our study focuses on local information algorithms --- sequential algorithms where the network topology is initially unknown and is revealed only within a local neighborhood of vertices that have been irrevocably added to the output set. We address both network coverage problems as well as network search problems. Our results include local information algorithms for coverage problems whose performance closely match the best possible even when information about network structure is unrestricted. We also demonstrate a sharp threshold on the level of visibility required: at a certain visibility level it is possible to design algorithms that nearly match the best approximation possible even with full access to the network structure, but with any less information it is impossible to achieve a reasonable approximation. For preferential attachment networks, we obtain polylogarithmic approximations to the problem of finding the smallest subgraph that connects a subset of nodes and the problem of finding the highest-degree nodes. This is achieved by addressing a decade-old open question of Bollobás and Riordan on locally finding the root in a preferential attachment process. In the second part of the dissertation we focus on designing highly time efficient local algorithms for central mining problems on complex networks that have been in the focus of the research community over a decade: finding a small set of influential nodes in the network, and fast ranking of nodes. Among our results is an essentially runtime-optimal local algorithm for the influence maximization problem in the standard independent cascades model of information diffusion and an essentially runtime-optimal local algorithm for the problem of returning all nodes with PageRank bigger than a given threshold. Our work demonstrates that locality is powerful enough to allow efficient solutions to many central algorithmic problems on complex networks

SLIM : Scalable Linkage of Mobility Data

We present a scalable solution to link entities across mobility datasets using their spatio-temporal information. This is a fundamental problem in many applications such as linking user identities for security, understanding privacy limitations of location based services, or producing a unified dataset from multiple sources for urban planning. Such integrated datasets are also essential for service providers to optimise their services and improve business intelligence. In this paper, we first propose a mobility based representation and similarity computation for entities. An efficient matching process is then developed to identify the final linked pairs, with an automated mechanism to decide when to stop the linkage. We scale the process with a locality-sensitive hashing (LSH) based approach that significantly reduces candidate pairs for matching. To realize the effectiveness and efficiency of our techniques in practice, we introduce an algorithm called SLIM. In the experimental evaluation, SLIM outperforms the two existing state-of-the-art approaches in terms of precision and recall. Moreover, the LSH-based approach brings two to four orders of magnitude speedup