منابع مشابه
Multicoloring Planar Graphs and Partial k-Trees
We study graph multicoloring problems, motivated by the scheduling of dependent jobs on multiple machines. In multicoloring problems, vertices have lengths which determine the number of colors they must receive, and the desired coloring can be either contiguous (non-preemptive schedule) or arbitrary (preemptive schedule). We consider both the sum-of-completion times measure, or the sum of the l...
متن کاملMinimum sum multicoloring on the edges of trees
The edge multicoloring problem is that given a graph G and integer demands x(e) for every edge e, assign a set of x(e) colors to edge e, such that adjacent edges have disjoint sets of colors. In the minimum sum edge multicoloring problem the finish time of an edge is defined to be the highest color assigned to it. The goal is to minimize the sum of the finish times. The main result of the paper...
متن کاملEdge list multicoloring trees: An extension of Hall's theorem
We prove a necessary and sufficient condition for the existence of edge list multicoloring of trees. The result extends the Halmos – Vaughan generalization of Hall’s theorem on the existence of distinct representatives of sets. ∗Supported by grant OTKA T029074 †On leave from the Computer and Automation Research Institute of the Hungarian Academy of Sciences
متن کاملMinimum Sum Multicoloring on the Edges of Trees: (Extended Abstract)
The edge multicoloring problem is that given a graph G and integer demands x(e) for every edge e, assign a set of x(e) colors to edge e, such that adjacent edges have disjoint sets of colors. In the minimum sum edge multicoloring problem the finish time of an edge is defined to be the highest color assigned to it. The goal is to minimize the sum of the finish times. The main result of the paper...
متن کاملImproved Distributed Algorithms for Coloring Interval Graphs with Application to Multicoloring Trees
We give a distributed (1+ )-approximation algorithm for the minimum vertex coloring problem on interval graphs, which runs in the LOCAL model and operates in O( 1 log∗ n) rounds. If nodes are aware of their interval representations, then the algorithm can be adapted to the CONGEST model using the same number of rounds. Prior to this work, only constant factor approximations using O(log∗ n) roun...
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ژورنال
عنوان ژورنال: Information and Computation
سال: 2003
ISSN: 0890-5401
DOI: 10.1016/s0890-5401(02)00032-9