Edge coloring with delays

Noga Alon, Vera Asodi

Research output: Chapter in Book/Report/Conference proceedingChapter

1 Scopus citations

Abstract

Consider the following communication problem, that leads to a new notion of edge coloring. The communication network is represented by a bipartite multigraph, where the nodes on one side are the transmitters and the nodes on the other side are the receivers. The edges correspond to messages, and every edge e is associated with an integer c(e), corresponding to the time it takes the message to reach its destination. A proper k-edge-coloring with delays is a function f from the edges to {0,1,..., k-1), such that for every two edges e1 and e2 with the same transmitter, f(e1) ≠ f(e2), and for every two edges e1 and e2 with the same receiver, f(e1)+c(e1) ≢ f(e2) + c(e2) (mod k). Haxell, Wilfong and Winkler [10] conjectured that there always exists a proper edge coloring with delays using k = Δ + 1 colors, where Δ is the maximum degree of the graph. We prove that the conjecture asymptotically holds for simple bipartite graphs, using a probabilistic approach, and further show that it holds for some multigraphs, applying algebraic tools. The probabilistic proof provides an efficient algorithm for the corresponding algorithmic problem, whereas the algebraic method does not.

Original languageEnglish (US)
Title of host publicationLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
EditorsKlaus Jansen, Sanjeev Khanna, Jose D. P. Rolim, Dana Ron
PublisherSpringer Verlag
Pages237-248
Number of pages12
ISBN (Print)3540228942, 9783540228943
DOIs
StatePublished - 2004
Externally publishedYes

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume3122
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349

All Science Journal Classification (ASJC) codes

  • Theoretical Computer Science
  • Computer Science(all)

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