Search

In this paper, we consider the perfect demand matching problem (PDM) which combines aspects of the knapsack problem along with the b -matching problem. It is a generalization of the maximum weight matching problem which has been fundamental in the development of theory of computer science and operations research. This problem is NP-hard and there exists a constant ϵ > 0 such that the problem admits no 1 + ϵ -approximation algorithm, unless P=NP. Here, we investigate the performance of a distributed message passing algorithm called Max-sum belief propagation for computing the problem of finding the optimal perfect demand matching. As the main result, we demonstrate the rigorous theoretical analysis of the Max-sum BP algorithm for PDM , and establish that within pseudo-polynomial-time, our algorithm could converge to the optimal solution of PDM , provided that the optimal solution of its LP relaxation is unique and integral. Different from the techniques used in previous literature, our analysis is based on primal-dual complementary slackness conditions, and thus the number of iterations of the algorithm is independent of the structure of the given graph. Moreover, to the best of our knowledge, this is one of a very few instances where BP algorithm is proved correct for NP-hard problems. • The perfect demand matching problem (PDM) is NP-hard and MAXSNP-complete. • Demonstrate the rigorous theoretical analysis of Max-sum belief propagation for PDM. • The algorithm converges to the optimal solution of PDM within pseudo-polynomial time. • Our analysis is based on primal-dual complementary slackness conditions. [ABSTRACT FROM AUTHOR]

Abstract: The ability to provide uniform shared-memory access to a significant number of processors in a single SMP node brings us much closer to the ideal PRAM parallel computer. Many PRAM algorithms can be adapted to SMPs with few modifications. Yet there are few studies that deal with the implementation and performance issues of running PRAM-style algorithms on SMPs. Our study in this paper focuses on implementing parallel spanning tree algorithms on SMPs. Spanning tree is an important problem in the sense that it is the building block for many other parallel graph algorithms and also because it is representative of a large class of irregular combinatorial problems that have simple and efficient sequential implementations and fast PRAM algorithms, but these irregular problems often have no known efficient parallel implementations. Experimental studies have been conducted on related problems (minimum spanning tree and connected components) using parallel computers, but only achieved reasonable speedup on regular graph topologies that can be implicitly partitioned with good locality features or on very dense graphs with limited numbers of vertices. In this paper we present a new randomized algorithm and implementation with superior performance that for the first time achieves parallel speedup on arbitrary graphs (both regular and irregular topologies) when compared with the best sequential implementation for finding a spanning tree. This new algorithm uses several techniques to give an expected running time that scales linearly with the number p of processors for suitably large inputs (). As the spanning tree problem is notoriously hard for any parallel implementation to achieve reasonable speedup, our study may shed new light on implementing PRAM algorithms for shared-memory parallel computers. The main results of this paper are [1.] A new and practical spanning tree algorithm for symmetric multiprocessors that exhibits parallel speedups on graphs with regular and irregular topologies; and [2.] an experimental study of parallel spanning tree algorithms that reveals the superior performance of our new approach compared with the previous algorithms. The source code for these algorithms is freely-available from our web site. [Copyright &y& Elsevier]

Abstract: This paper shows that shared-coin algorithms can be combined to optimize several complexity measures, even in the presence of a strong adversary. By combining shared coins of Bracha and Rachman (1991)  and of Aspnes and Waarts (1996) , this yields a shared-coin algorithm, and hence, a randomized consensus algorithm, with individual work and total work, using single-writer registers. This improves upon each of the above shared coins (where the former has a high cost for individual work, while the latter reduces it but pays in the total work), and is currently the best for this model. Another application is to prove a construction of Saks, Shavit, and Woll (1991) , which combines a shared-coin algorithm that takes time in failure-free executions, with one that takes time in executions where at most processes fail, and another one that takes time in any other execution. [Copyright &y& Elsevier]

Abstract: In this paper, we focus on the perimeter detection problem using wireless sensor networks, as perimeter detection has a wide range of uses in several areas. We present a decentralized localized algorithm where sensor nodes determine if they are located along the perimeter of a wireless sensor network. Our proposed algorithm uses the location neighborhood information in conjunction with the Barycentric technique to determine if the sensor node enclosed by neighboring nodes, and consequently, if it is located within the interior of the wireless sensor network. We define performance metrics to analyze the performance of our approach and the simulation shows that the algorithm gives fairly accurate results. [Copyright &y& Elsevier]