Distributed Graph Algorithms

This chapter addresses three basic graph problems encountered in the context of distributed systems. These problems are (a) the computation of the shortest paths between a pair of processes where a positive length (or weight) is attached to each communication channel, (b) the coloring of the vertices (processes) of a graph in Δ+1 colors (where Δ is the maximal number of neighbors of a process, i.e., the maximal degree of a vertex when using the graph terminology), and (c) the detection of knots and cycles in a graph. As for the previous chapter devoted to graph traversal algorithms, an aim of this chapter is not only to present specific distributed graph algorithms, but also to show that their design is not always obtained from a simple extension of their sequential counterparts.

[1]  Leonid Barenboim,et al.  Deterministic Distributed Vertex Coloring in Polylogarithmic Time , 2011, J. ACM.

[2]  K. Mani Chandy,et al.  Distributed computation on graphs: shortest path algorithms , 1982, CACM.

[3]  D. Manivannan,et al.  An Efficient Distributed Algorithm for Detection of Knots and Cycles in a Distributed Graph , 2003, IEEE Trans. Parallel Distributed Syst..

[4]  Stephen Warshall,et al.  A Theorem on Boolean Matrices , 1962, JACM.

[5]  A. Gibbons.  Algorithmic Graph Theory , 1985 .

[6]  Ajay D. Kshemkalyani,et al.  Distributed Computing: Principles, Algorithms, and Systems , 2008 .

[7]  Ajay D. Kshemkalyani,et al.  Distributed Computing: Index , 2008 .

[8]  K. Mani Chandy,et al.  A Distributed Graph Algorithm: Knot Detection , 1982, TOPL.

[9]  Öjvind Johansson.  Simple Distributed Delta+1-coloring of Graphs , 1999, Inf. Process. Lett..

[10]  R. Bellman.  Dynamic programming. , 1957, Science.

[11]  Azzedine Boukerche,et al.  A Distributed Graph Algorithm for the Detection of Local Cycles and Knots , 1998, IEEE Trans. Parallel Distributed Syst..

[12]  David S. Johnson,et al.  Computers and Intractability: A Guide to the Theory of NP-Completeness , 1978 .

[13]  Michael Luby.  A Simple Parallel Algorithm for the Maximal Independent Set Problem , 1986, SIAM J. Comput..

[14]  Nicola Santoro,et al.  Distributed algorithms for finding centers and medians in networks , 1984, TOPL.

[15]  Israel Cidon.  An Efficient Distributed Knot Detection Algorithm , 1989, IEEE Trans. Software Eng..

[16]  Shimon Even,et al.  Graph Algorithms: Contents , 2011 .