Message and time efficient multi-broadcast schemes

We consider message and time efficient broadcasting and multi-broadcasting in wireless ad-hoc networks, where a subset of nodes, each with a unique rumor, wish to broadcast their rumors to all destinations while minimizing the total number of transmissions and total time until all rumors arrive to their destination. Under centralized settings, we introduce a novel approximation algorithm that provides almost optimal results with respect to the number of transmissions and total time, separately. Later on, we show how to efficiently implement this algorithm under distributed settings, where the nodes have only local information about their surroundings. In addition, we show multiple approximation techniques based on the network collision detection capabilities and explain how to calibrate the algorithms' parameters to produce optimal results for time and messages.Comment: In Proceedings FOMC 2013, arXiv:1310.459

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

Building Damage-Resilient Dominating Sets in Complex Networks against Random and Targeted Attacks

We study the vulnerability of dominating sets against random and targeted node removals in complex networks. While small, cost-efficient dominating sets play a significant role in controllability and observability of these networks, a fixed and intact network structure is always implicitly assumed. We find that cost-efficiency of dominating sets optimized for small size alone comes at a price of being vulnerable to damage; domination in the remaining network can be severely disrupted, even if a small fraction of dominator nodes are lost. We develop two new methods for finding flexible dominating sets, allowing either adjustable overall resilience, or dominating set size, while maximizing the dominated fraction of the remaining network after the attack. We analyze the efficiency of each method on synthetic scale-free networks, as well as real complex networks

GraphCombEx: A Software Tool for Exploration of Combinatorial Optimisation Properties of Large Graphs

We present a prototype of a software tool for exploration of multiple combinatorial optimisation problems in large real-world and synthetic complex networks. Our tool, called GraphCombEx (an acronym of Graph Combinatorial Explorer), provides a unified framework for scalable computation and presentation of high-quality suboptimal solutions and bounds for a number of widely studied combinatorial optimisation problems. Efficient representation and applicability to large-scale graphs and complex networks are particularly considered in its design. The problems currently supported include maximum clique, graph colouring, maximum independent set, minimum vertex clique covering, minimum dominating set, as well as the longest simple cycle problem. Suboptimal solutions and intervals for optimal objective values are estimated using scalable heuristics. The tool is designed with extensibility in mind, with the view of further problems and both new fast and high-performance heuristics to be added in the future. GraphCombEx has already been successfully used as a support tool in a number of recent research studies using combinatorial optimisation to analyse complex networks, indicating its promise as a research software tool

Upper bounds for alpha-domination parameters

In this paper, we provide a new upper bound for the alpha-domination number. This result generalises the well-known Caro-Roditty bound for the domination number of a graph. The same probabilistic construction is used to generalise another well-known upper bound for the classical domination in graphs. We also prove similar upper bounds for the alpha-rate domination number, which combines the concepts of alpha-domination and k-tuple domination.Comment: 7 pages; Presented at the 4th East Coast Combinatorial Conference, Antigonish (Nova Scotia, Canada), May 1-2, 200

An Efficient Streaming Algorithm for the Submodular Cover Problem

We initiate the study of the classical Submodular Cover (SC) problem in the data streaming model which we refer to as the Streaming Submodular Cover (SSC). We show that any single pass streaming algorithm using sublinear memory in the size of the stream will fail to provide any non-trivial approximation guarantees for SSC. Hence, we consider a relaxed version of SSC, where we only seek to find a partial cover. We design the first Efficient bicriteria Submodular Cover Streaming (ESC-Streaming) algorithm for this problem, and provide theoretical guarantees for its performance supported by numerical evidence. Our algorithm finds solutions that are competitive with the near-optimal offline greedy algorithm despite requiring only a single pass over the data stream. In our numerical experiments, we evaluate the performance of ESC-Streaming on active set selection and large-scale graph cover problems.Comment: To appear in NIPS'1