A coloring problem for weighted graphs
Information Processing Letters
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
Scheduling Algorithms
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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
Improved approximation algorithms for the max-edge coloring problem
TAPAS'11 Proceedings of the First international ICST conference on Theory and practice of algorithms in (computer) systems
Improved approximation algorithms for the Max Edge-Coloring problem
Information Processing Letters
Clique clustering yields a PTAS for max-coloring interval graphs
ICALP'11 Proceedings of the 38th international colloquim conference on Automata, languages and programming - Volume Part I
Theoretical Computer Science
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The max-coloring problem is to compute a legal coloring of the vertices of a graph G = (V,E) with a non-negative weight function w on V such that $\sum_{i=1}^k \max_{v\in C_i} w(v_i)$ is minimized, where C 1,...,C k are the various color classes. Max-coloring general graphs is as hard as the classical vertex coloring problem, a special case 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 a broad class of trees and show it can be solved in time $O(|V| + \text{time for sorting the vertex weights})$. When vertex weights belong to 驴, we show a matching lower bound of 驴(|V|log|V|) in the algebraic computation tree model.