This paper addresses the state explosion problem in automata based LTL model checking. To deal with large space requirements we turn to use a distributed approach. All the known methods for automata based model checking are based on depth first traversal of the state space which is difficult to parallelise as the ordering in which vertices are visited plays an important role. We come up with entirely different approach which is dependent on locating cycles with negative length in a directed graph with real number length of edges. Our method allows reasonable distribution and the experimental results confirm its usefulness for distributed model checking.

A distributed algorithm for the single source shortest path problem for directed graphs with arbitrary edge lengths is proposed. The new algorithm is based on relaxations and uses reverse search for inspecting edges and thus avoids using any additional data structures. At the same time the algorithm uses a novel way to recognize a reachable negative-length cycle in the graph which facilitates the scalability of the algorithm.

Abstract—Energy conservation is an important concern in wireless networks. Many algorithms for constructing a broadcast tree with minimum energy consumption and other goals have been developed. However, no previous research work considers the total energy consumption and transmission delays of the broadcast tree simultaneously. In this paper, based on anð; Þ-tree, a novel concept to wireless networks, we define a new Strongly connected Broadcast Arborescence with bounded Transmission delay (SBAT) problem and design the Strongly connected Broadcast Arborescence (SBA) algorithm with linear running time to construct a strongly connected broadcast tree with bounded total power, while satisfying the constraint that the transmission delays between the source and the other hosts are also bounded. We also propose the distributed version of the SBA algorithm. The theoretical analysis and simulation results show that the SBA algorithm gives a proper solution to the SBAT problem. Index Terms—Wireless networks, routing protocols, network management, distributed applications, algorithm design and analysis. 1

Several new distributed algorithms for the single source shortest paths and for the negative cycle detection problems on arbitrary directed graphs given by adjacency list are developed, theoretically analysed, proved correct, and experimentally compared. The algorithms are to be performed on clusters of workstations that communicate via a message passing mechanism.