On the complexity of distributed graph coloring with local minimality constraints

Distributed greedy coloring is an interesting and intuitive variation of the standard coloring problem. Given an order among the colors, a coloring is said to be greedy if there does not exist a vertex for which its associated color can be replaced by a color of lower position in the fixed order without violating the property that neighboring vertices must receive different colors. We consider the problems of Greedy Coloring and Largest First Coloring (a variant of greedy coloring with strengthened constraints) in the Linial model of distributed computation, providing lower and upper bounds and a comparison to the ( + 1)-Coloring and Maximal Independent Set problems, with being the maximum vertex degree in G. © 2009 Wiley Periodicals, Inc. NETWORKS, Vol. 54(1), 12–19 2009

[1]  Alfredo Navarra,et al.  On the Complexity of Distributed Greedy Coloring , 2007, DISC.

[2]  Andrew V. Goldberg,et al.  Network decomposition and locality in distributed computation , 1989, 30th Annual Symposium on Foundations of Computer Science.

[3]  David S. Johnson,et al.  Computers and In stractability: A Guide to the Theory of NP-Completeness. W. H Freeman, San Fran , 1979 .

[4]  Roberto Battiti,et al.  Assigning codes in wireless networks: bounds and scaling properties , 1999, Wirel. Networks.

[5]  Alessandro Panconesi,et al.  Fast distributed algorithms for Brooks-Vizing colourings , 2000, SODA '98.

[6]  A. Leaf.  GRAPH THEORY AND PROBABILITY , 1957 .

[7]  Jonathan S. Turner,et al.  Almost All k-Colorable Graphs are Easy to Color , 1988, J. Algorithms.

[8]  Stephan Olariu,et al.  Welsh-Powell Opposition Graphs , 1989, Inf. Process. Lett..

[9]  Alessandro Panconesi,et al.  Some simple distributed algorithms for sparse networks , 2001, Distributed Computing.

[10]  Gabriele Di Stefano,et al.  Track assignment , 2007, J. Discrete Algorithms.

[11]  Pranay Chaudhuri.  Algorithms for some graph problems on a distributed computational model , 1987, Inf. Sci..

[12]  Aravind Srinivasan,et al.  On the Complexity of Distributed Network Decomposition , 1996, J. Algorithms.

[13]  Thomas Moscibroda,et al.  What Cannot Be Computed Locally , 2004 .

[14]  Nathan Linial.  Legal coloring of graphs , 1986, Comb..

[15]  Roger Wattenhofer,et al.  A log-star distributed maximal independent set algorithm for growth-bounded graphs , 2008, PODC '08.

[16]  Adam Nadolski,et al.  Distributed Largest-First Algorithm for Graph Coloring , 2004, Euro-Par.

[17]  David Zuckerman,et al.  Electronic Colloquium on Computational Complexity, Report No. 100 (2005) Linear Degree Extractors and the Inapproximability of MAX CLIQUE and CHROMATIC NUMBER , 2005 .

[18]  Alessandro Panconesi,et al.  An Experimental Analysis of Simple, Distributed Vertex Coloring Algorithms , 2002, SODA '02.

[19]  Alfredo Navarra,et al.  Managing Random Sensor Networks by means of Grid Emulation , 2006, Networking.

[20]  Michael Luby,et al.  A simple parallel algorithm for the maximal independent set problem , 1985, STOC '85.

[21]  Nathan Linial,et al.  Locality in Distributed Graph Algorithms , 1992, SIAM J. Comput..

[22]  Mirka Miller,et al.  The train marshalling problem , 2000, Discret. Appl. Math..

[23]  Daniele Frigioni,et al.  Robust Algorithms and Price of Robustness in Shunting Problems , 2007, ATMOS.

[24]  Roger Wattenhofer,et al.  On the complexity of distributed graph coloring , 2006, PODC '06.

[25]  Adrian Kosowski,et al.  On Greedy Graph Coloring in the Distributed Model , 2006, Euro-Par.