Using dual approximation algorithms for scheduling problems theoretical and practical results
Journal of the ACM (JACM)
PODC '88 Proceedings of the seventh annual ACM Symposium on Principles of distributed computing
Deterministic decomposition of recursive graph classes
SIAM Journal on Discrete Mathematics
Scheduling problems in parallel query optimization
PODS '95 Proceedings of the fourteenth ACM SIGACT-SIGMOD-SIGART symposium on Principles of database systems
A Linear-Time Algorithm for Finding Tree-Decompositions of Small Treewidth
SIAM Journal on Computing
A partial k-arboretum of graphs with bounded treewidth
Theoretical Computer Science
Fast Approximation Algorithms for the Knapsack and Sum of Subset Problems
Journal of the ACM (JACM)
Computers and Intractability: A Guide to the Theory of NP-Completeness
Computers and Intractability: A Guide to the Theory of NP-Completeness
Treewidth: Algorithmoc Techniques and Results
MFCS '97 Proceedings of the 22nd International Symposium on Mathematical Foundations of Computer Science
VLDB '94 Proceedings of the 20th International Conference on Very Large Data Bases
Linear algorithms on k-terminal graphs
Linear algorithms on k-terminal graphs
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We investigate a class of scheduling problems that arise in the optimization of SQL queries for parallel machines (Chekuri et al. in PODS'95, pp. 255---265, 1995). In these problems, an undirected graph is used to represent communication and inter-operator parallelism. The goal is to minimize the global response time of the system.We provide a polynomial time approximation scheme for the special cases where the operator graph is a tree, thereby improving on a polynomial time 2.87-approximation algorithm by Chekuri et al. The approximation scheme is generalized to the case where the operator graph has treewidth bounded by a constant. We analyze instances with small response times for general operator graphs: Deciding whether a response time of four time units can be reached is easy, but deciding whether a response time of six time units can be reached is NP-hard. Finally, we prove that for general operator graphs the existence of a polynomial time approximation algorithm with worst case performance guarantee better than 4/3 would imply P=NP.