Edge- and Node-Disjoint Paths in P Systems

In this paper, we continue our development of algorithms used for topological network discovery. We present native P system versions of two fundamental problems in graph theory: finding the maximum number of edge- and node-disjoint paths between a source node and target node. We start from the standard depth-first-search maximum flow algorithms, but our approach is totally distributed, when initially no structural information is available and each P system cell has to even learn its immediate neighbors. For the node-disjoint version, our P system rules are designed to enforce node weight capacities (of one), in addition to edge capacities (of one), which are not readily available in the standard network flow algorithms.

[1]  Gheorghe Paun,et al.  Introduction to Membrane Computing , 2006, Applications of Membrane Computing.

[2]  Richard M. Karp,et al.  Theoretical Improvements in Algorithmic Efficiency for Network Flow Problems , 1972, Combinatorial Optimization.

[3]  Gheorghe Paun,et al.  Membrane computing and programming , 2010, J. Log. Algebraic Methods Program..

[4]  Ioan Dzitac,et al.  60 Years from Birth of Academician F.G. Filip , 2007, Int. J. Comput. Commun. Control.

[5]  D. R. Fulkerson,et al.  Maximal Flow Through a Network , 1956 .

[6]  Radu Nicolescu,et al.  A Faster P Solution for the Byzantine Agreement Problem , 2010, Int. Conf. on Membrane Computing.

[7]  Radu Nicolescu,et al.  New Solutions to the Firing Squad Synchronization Problems for Neural and Hyperdag P Systems , 2009, MeCBIC.

[8]  Paul D. Seymour,et al.  Graph Minors: XV. Giant Steps , 1996, J. Comb. Theory, Ser. B.

[9]  Seif Haridi,et al.  Distributed Algorithms , 1992, Lecture Notes in Computer Science.

[10]  Radu Nicolescu,et al.  Towards Structured Modelling with Hyperdag P Systems , 2010, Int. J. Comput. Commun. Control.

[11]  Radu Nicolescu,et al.  Discovering the Membrane Topology of Hyperdag P Systems , 2009, Workshop on Membrane Computing.

[12]  Radu Nicolescu,et al.  P systems and the Byzantine agreement , 2010, J. Log. Algebraic Methods Program..

[13]  Gheorghe Paun,et al.  Membrane Computing , 2002, Natural Computing Series.

[14]  Neil Robertson,et al.  Graph Minors .XIII. The Disjoint Paths Problem , 1995, J. Comb. Theory B.

[15]  Mithuna Thottethodi,et al.  Disjoint-path routing: Efficient communication for streaming applications , 2009, 2009 IEEE International Symposium on Parallel & Distributed Processing.

[16]  K. Menger Zur allgemeinen Kurventheorie , 1927 .

[17]  Alfonso Rodríguez-Patón,et al.  Tissue P systems , 2003, Theor. Comput. Sci..

[18]  Gheorghe Paun,et al.  Computing with Membranes , 2000, J. Comput. Syst. Sci..

[19]  Radu Nicolescu,et al.  Structured Modelling with Hyperdag~P~Systems: Part B , 2009 .