We present a natural greedy algorithm for the metric uncapacitated facility location problem and use the method of dual fitting to analyze its approximation ratio, which turns out to be 1.861. The running time of our algorithm is O(m log m), where m is the total number of edges in the underlying complete bipartite graph between cities and facilities. We use our algorithm to improve recent results for some variants of the problem, such as the fault tolerant and outlier versions. In addition, we introduce a new variant which can be seen as a special case of the concave cost version of this problem.

Network querying is a growing domain with vast applications ranging from screening compounds against a database of known molecules to matching sub-networks across species. Graph indexing is a powerful method for searching a large database of graphs. Most graph indexing methods to date tackle the exact matching (isomorphism) problem, limiting their applicability to specific instances in which such matches exist. Here we provide a novel graph indexing method to cope with the more general, inexact matching problem. Our method, SIGMA, builds on approximating a variant of the set-cover problem that concerns overlapping multi-sets. We extensively test our method and compare it to a baseline method and to the state-of-the-art Grafil. We show that SIGMA outperforms both, providing higher pruning power in all the tested scenarios.

Abstract. Given a universe N containing n elements and a collection of multisets or sets over N, the multiset multicover (MSMC) or the set multicover (SMC) problem is to cover all elements at least a number of times as specified in their coverage requirements with the minimum number of multisets or sets. In this paper, we give various exact algorithms for these two problems, with or without constraints on the number of times a multiset or set may be picked. First, we can exactly solve the MSMC without multiplicity constraints problem in O(((b +1)(c +1)) n) time where b and c (c ≤ b and b ≥ 2) respectively are the maximum coverage requirement and the maximum number of times that each element can appear in a multiset. To our knowledge, this is the first known exact algorithm for the MSMC without multiplicity constraints problem. Second, we can solve the SMC without multiplicity constraints problem in O((b +2) n) time. Compared with the two recent results in [Hua et al., Set Multi-covering via inclusion-exclusion, Theoretical Computer Science, 410(38-40):3882-3892 (2009)] and [Nederlof, J.: Inclusion Exclusion

Abstract. We consider setting up sleep scheduling in sensor networks. We formulate the problem as an instance of the fractional domatic partition problem and obtain a distributed approximation algorithm by applying linear programming approximation techniques. Our algorithm is an application of the Garg-Könemann (GK) scheme that requires solving an instance of the minimum weight dominating set (MWDS) problem as a subroutine. Our two main contributions are a distributed implementation of the GK scheme for the sleep-scheduling problem and a novel asynchronous distributed algorithm for approximating MWDS based on a primal-dual analysis of Chvátal’s set-cover algorithm. We evaluate our algorithm with ns2 simulations. 1

Abstract In social networks, there is a tendency for connected users to match each other’s behaviors. Moreover, a user likely adopts a behavior, if a certain fraction of his family and friends follows that behavior. Identifying people who have the most influential effect to the others is of great advantages, especially in politics, marketing, behavior correction, and so on. Under a graph-theoretical framework, we study the positive influence dominating set (PIDS) problem that seeks for a minimal set of nodes P such that all other nodes in the network have at least a fraction ρ> 0 of their neighbors in P. We also study a different formulation, called total positive influence dominating set (TPIDS), in which even nodes in P are required to have a fraction ρ of neighbors inside P. We show that neither of these problems can be approximated within a factor of (1−ɛ) ln max{∆, |V | 1/2}, where ∆ is the maximum degree. Moreover, we provide a simple proof that both problems can be approximated within a factor ln ∆ + O(1). In power-law networks, where the degree sequence follows a power-law distribution, both problems admit constant factor approximation algorithms. Finally, we present a linear-time exact algorithms for trees.