Distributed Negative Cycle Detection Algorithms

نویسندگان

  • Lubos Brim
  • Ivana Cerná
  • Lukás Hejtmánek
چکیده

The single source shortest path problem (SSSP) is a fundamental problem with many theoretical and practical applications and with several effective and well-grounded sequential algorithms. The same can be said about the closely related negative cycle problem (NCP) which is to find a negative length cycle in a graph or to prove that there are none. In fact, all known algorithms for NCP combine a shortest paths algorithm with some cycle detection strategy. In many applications we have to deal with extremely large graphs (a particular application we have in mind is briefly discussed bellow). Whenever a graph is too large to fit into memory that is randomly accessed a memory that is sequentially accessed has to be employed. This causes a bottleneck in the performance of a sequential algorithm owing to the significant amount of paging involved during its execution. A usual approach to deal with these practical limitations is to increase the computational power (especially randomly accessed memory) by building a powerful (yet cheap) distributed-memory cluster of computers. The computers are programmed in single-program, multiple-data style, meaning that one program runs concurrently on each processor and its execution is specialised for each processor by using its processor identity (id). Parallel programs rely on communication layer based on Message-Passing Interface standard. Our motivation for this work was to develop a distributed model checking algorithm for linear temporal logic[BČKP01b] which can be reduced to the negative cycle problem.

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تاریخ انتشار 2003