The linearity of first-fit coloring of interval graphs
SIAM Journal on Discrete Mathematics
An on-line graph coloring algorithm with sublinear performance ratio
Discrete Mathematics
Coloring interval graphs with First-Fit
Discrete Mathematics
A coloring problem for weighted graphs
Information Processing Letters
Buffer minimization using max-coloring
SODA '04 Proceedings of the fifteenth annual ACM-SIAM symposium on Discrete algorithms
Time slot scheduling of compatible jobs
Journal of Scheduling
Weighted Coloring: further complexity and approximability results
Information Processing Letters
Online interval coloring and variants
ICALP'05 Proceedings of the 32nd international conference on Automata, Languages and Programming
Approximation algorithms for the max-coloring problem
ICALP'05 Proceedings of the 32nd international conference on Automata, Languages and Programming
Weighted coloring on planar, bipartite and split graphs: complexity and improved approximation
ISAAC'04 Proceedings of the 15th international conference on Algorithms and Computation
Batch Coloring Flat Graphs and Thin
SWAT '08 Proceedings of the 11th Scandinavian workshop on Algorithm Theory
Weighted coloring on planar, bipartite and split graphs: Complexity and approximation
Discrete Applied Mathematics
Max-Coloring Paths: Tight Bounds and Extensions
ISAAC '09 Proceedings of the 20th International Symposium on Algorithms and Computation
Approximating the max-edge-coloring problem
Theoretical Computer Science
Return of the boss problem: competing online against a non-adaptive adversary
FUN'10 Proceedings of the 5th international conference on Fun with algorithms
Max-coloring and online coloring with bandwidths on interval graphs
ACM Transactions on Algorithms (TALG)
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
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
Max-coloring paths: tight bounds and extensions
Journal of Combinatorial Optimization
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We consider max coloring on hereditary graph classes. The problem is defined as follows. Given a graph G = (V,E) and positive node weights w : V → (1,∞), the goal is to find a proper node coloring of G whose color classes C1,C2,...,Ck minimize σi=1k maxυ∈Ci w(v). We design a general framework which allows to convert approximation algorithms for standard node coloring into algorithms for max coloring. The approximation ratio increases by a multiplicative factor of at most e for deterministic offline algorithms and for randomized online algorithms, and by a multiplicative factor of at most 4 for deterministic online algorithms. We consider two specific hereditary classes which are interval graphs and perfect graphs. For interval graphs, we study the problem in several online environments. In the List Model, intervals arrive one by one, in some order. In the Time Model, intervals arrive one by one, sorted by their left endpoint. For the List Model we design a deterministic 12-competitive algorithm, a randomized 3e-competitive algorithm, and prove a lower bound of 4 on the (deterministic or randomized) competitive ratio. For the Time Model, we use simplified versions of the algorithm and the lower bound of the List Model, to achieve a deterministic 4-competitive algorithm, a randomized e-competitive algorithm, and lower bounds of φ ≅ 1.618 on the deterministic competitive ratio and 4/3 on the randomized competitive ratio. The former lower bounds hold even for unit intervals. For unit intervals in the List Model, we obtain a deterministic 8-competitive algorithm, a randomized 2e-competitive algorithm and lower bounds of 2 on the deterministic competitive ratio and 11/6 ≅ 1.8333 on the randomized competitive ratio. Finally, we employ our framework to obtain an offline e-approximation algorithm for max coloring of perfect graphs, improving and simplifying a recent result of Pemmaraju and Raman.