New methods to color the vertices of a graph
Communications of the ACM
Computers and Intractability: A Guide to the Theory of NP-Completeness
Computers and Intractability: A Guide to the Theory of NP-Completeness
A Heuristic Method for the Set Covering Problem
Operations Research
Reactive GRASP: An Application to a Matrix Decomposition Problem in TDMA Traffic Assignment
INFORMS Journal on Computing
Performance of Various Computers Using Standard Linear Equations Software
Performance of Various Computers Using Standard Linear Equations Software
Weighted coloring: further complexity and approximability results
Information Processing Letters
Time slot scheduling of compatible jobs
Journal of Scheduling
A Set-Covering-Based Heuristic Approach for Bin-Packing Problems
INFORMS Journal on Computing
A Metaheuristic Approach for the Vertex Coloring Problem
INFORMS Journal on Computing
Buffer sharing in CSP-like programs
MEMOCODE'09 Proceedings of the 7th IEEE/ACM international conference on Formal Methods and Models for Codesign
Algorithms for the Bin Packing Problem with Conflicts
INFORMS Journal on Computing
Buffer sharing in rendezvous programs
IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems - Special section on the ACM IEEE international conference on formal methods and models for codesign (MEMOCODE) 2009
A one-to-one correspondence between colorings and stable sets
Operations Research Letters
Optimising multi-rate link scheduling for wireless mesh networks
Computer Communications
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We consider a weighted version of the well-known Vertex Coloring Problem (VCP) in which each vertex i of a graph G has associated a positive weight w i . Like in VCP, one is required to assign a color to each vertex in such a way that colors on adjacent vertices are different, and the objective is to minimize the sum of the costs of the colors used. While in VCP the cost of each color is equal to one, in the Weighted Vertex Coloring Problem (WVCP) the cost of each color depends on the weights of the vertices assigned to that color, and it equals the maximum of these weights. WVCP is known to be NP-hard and arises in practical scheduling applications, where it is also known as Scheduling on a Batch Machine with Job Compatibilities. We propose three alternative Integer Linear Programming (ILP) formulations for WVCP: one is used to derive, dropping integrality requirement for the variables, a tight lower bound on the solution value, while a second one is used to derive a 2-phase heuristic algorithm, also embedding fast refinement procedures aimed at improving the quality of the solutions found. Computational results on a large set of instances from the literature are reported.