Distributed operating systems
A coloring problem for weighted graphs
Information Processing Letters
Efficiency of a Good But Not Linear Set Union Algorithm
Journal of the ACM (JACM)
Integer Sorting in 0(n sqrt (log log n)) Expected Time and Linear Space
FOCS '02 Proceedings of the 43rd Symposium on Foundations of Computer Science
On slot reuse for isochronous services in DQDB networks
RTSS '95 Proceedings of the 16th IEEE Real-Time Systems Symposium
Scheduling Algorithms
Dynamic Co-Scheduling of Distributed Computation and Replication
CCGRID '06 Proceedings of the Sixth IEEE International Symposium on Cluster Computing and the Grid
Batch Coloring Flat Graphs and Thin
SWAT '08 Proceedings of the 11th Scandinavian workshop on Algorithm Theory
Weighted Coloring: further complexity and approximability results
Information Processing Letters
WAOA'07 Proceedings of the 5th international conference on Approximation and online algorithms
Approximation algorithms for the max-coloring problem
ICALP'05 Proceedings of the 32nd international conference on Automata, Languages and Programming
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The max-coloring problem is to compute a legal coloring of the vertices of a graph G=(V,E) with vertex weights w such that $\sum_{i=1}^{k}\max_{v\in C_{i}}w(v_{i})$ is minimized, where C 1,驴,C k are the various color classes. For general graphs, max-coloring is as hard as the classical vertex coloring problem, a special case of the former where vertices have unit weight. In fact, in some cases it can even be harder: for example, no polynomial time algorithm is known for max-coloring trees. In this paper we consider the problem of max-coloring paths and its generalization, max-coloring skinny trees, a broad class of trees that includes paths and spiders. For these graphs, we show that max-coloring can be solved in time O(|V|+time for sorting the vertex weights). When vertex weights are real numbers, we show a matching lower bound of 驴(|V|log驴|V|) in the algebraic computation tree model.