Bounded vertex colorings of graphs
Discrete Mathematics
Scheduling with incompatible jobs
Discrete Applied Mathematics
Fixed-Parameter Tractability and Completeness I: Basic Results
SIAM Journal on Computing
Restrictions of graph partition problems. Part I
Theoretical Computer Science
The hardness of approximation: gap location
Computational Complexity
Scheduling Parallel Machines On-line
SIAM Journal on Computing
Theoretical Computer Science
Approximation of k-set cover by semi-local optimization
STOC '97 Proceedings of the twenty-ninth annual ACM symposium on Theory of computing
Zero knowledge and the chromatic number
Journal of Computer and System Sciences - Eleventh annual conference on structure and complexity 1996
Journal of Algorithms
Computers and Intractability: A Guide to the Theory of NP-Completeness
Computers and Intractability: A Guide to the Theory of NP-Completeness
On the Complexity of Scheduling Incompatible Jobs with Unit-Times
MFCS '93 Proceedings of the 18th International Symposium on Mathematical Foundations of Computer Science
On Complexity of Some Chain and Antichain Partition Problems
WG '91 Proceedings of the 17th International Workshop
The mutual exclusion scheduling problem for permutation and comparability graphs
Information and Computation
Information and Computation
Polynomial time approximation schemes for general multiprocessor job shop scheduling
Journal of Algorithms
OPT Versus LOAD in Dynamic Storage Allocation
SIAM Journal on Computing
Scheduling with conflicts on bipartite and interval graphs
Journal of Scheduling - Special issue: On-line scheduling
Linear degree extractors and the inapproximability of max clique and chromatic number
Proceedings of the thirty-eighth annual ACM symposium on Theory of computing
WAOA'06 Proceedings of the 4th international conference on Approximation and Online Algorithms
Scheduling jobs on identical machines with agreement graph
Computers and Operations Research
Bounds on contention management algorithms
Theoretical Computer Science
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We consider the following problem of scheduling with conflicts (swc): Find a minimum makespan schedule on identical machines where conflicting jobs cannot be scheduled concurrently. We study the problem when conflicts between jobs are modeled by general graphs.Our first main positive result is an exact algorithm for two machines and job sizes in {1,2}. For jobs sizes in {1,2,3}, we can obtain a $\frac{4}{3}$ -approximation, which improves on the $\frac{3}{2}$ -approximation that was previously known for this case. Our main negative result is that for jobs sizes in {1,2,3,4}, the problem is APX-hard.Our second contribution is the initiation of the study of an online model for swc, where we present the first results in this model. Specifically, we prove a lower bound of $2-\frac{1}{m}$ on the competitive ratio of any deterministic online algorithm for m machines and unit jobs, and an upper bound of 2 when the algorithm is not restricted computationally. For three machines we can show that an efficient greedy algorithm achieves this bound. For two machines we present a more complex algorithm that achieves a competitive ratio of $2-\frac{1}{7}$ when the number of jobs is known in advance to the algorithm.