Bounded vertex colorings of graphs
Discrete Mathematics
Restrictions of graph partition problems. Part I
Theoretical Computer Science
Approximation algorithms for NP-hard problems
Approximation algorithms for NP-hard problems
The mutual exclusion scheduling problem for permutation and comparability graphs
Information and Computation
Algorithmic Graph Theory and Perfect Graphs (Annals of Discrete Mathematics, Vol 57)
Algorithmic Graph Theory and Perfect Graphs (Annals of Discrete Mathematics, Vol 57)
Approximation algorithms for the max-coloring problem
ICALP'05 Proceedings of the 32nd international conference on Automata, Languages and Programming
Scheduling hybrid flowshop with parallel batching machines and compatibilities
Computers and Operations Research
Weighted coloring on planar, bipartite and split graphs: Complexity and approximation
Discrete Applied Mathematics
Discrete Applied Mathematics
Approximating the max-edge-coloring problem
Theoretical Computer Science
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
Scheduling an unbounded batching machine with job processing time compatibilities
Discrete Applied Mathematics
Capacitated max -batching with interval graph compatibilities
SWAT'10 Proceedings of the 12th Scandinavian conference on Algorithm Theory
A weakly robust PTAS for minimum clique partition in unit disk graphs
SWAT'10 Proceedings of the 12th Scandinavian conference on Algorithm Theory
A one-to-one correspondence between colorings and stable sets
Operations Research Letters
Theoretical Computer Science
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We analyze batch-scheduling problems that arise in connection with certain industrial applications. The models concern processing on a single max-batch machine with the additional feature that the tasks of the same batch have to be compatible. Compatibility is a symmetric binary relation-the compatible pairs are described with an undirected ''compatibility graph'', which is often an interval graph according to some natural practical conditions that we present. We consider several models with varying batch capacities, processing times or compatibility graphs. We summarize known results, and present a min-max formula and polynomial time algorithms.