Polynomial algorithms for graph isomorphism and chromatic index on partial k-trees
Journal of Algorithms
Easy problems for tree-decomposable graphs
Journal of Algorithms
Fast Approximation Algorithms for the Knapsack and Sum of Subset Problems
Journal of the ACM (JACM)
Linear-time computability of combinatorial problems on series-parallel graphs
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
Approximation algorithms for NP-hard optimization problems
Algorithms and theory of computation handbook
Approximability of partitioning graphs with supply and demand
ISAAC'06 Proceedings of the 17th international conference on Algorithms and Computation
On the complexity of reconfiguration problems
Theoretical Computer Science
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Suppose that each vertex of a graph G is either a supply vertex or a demand vertex and is assigned a positive real number, called the supply or the demand. Each demand vertex can receive ''power'' from at most one supply vertex through edges in G. One thus wishes to partition G into connected components by deleting edges from G so that each component C either has no supply vertex or has exactly one supply vertex whose supply is at least the sum of demands in C, and wishes to maximize the fulfillment, that is, the sum of demands in all components with supply vertices. This maximization problem is known to be NP-hard even for trees having exactly one supply vertex and strongly NP-hard for general graphs. In this paper, we focus on the approximability of the problem. We first show that the problem is MAXSNP-hard and hence there is no polynomial-time approximation scheme (PTAS) for general graphs unless P=NP. We then present a fully polynomial-time approximation scheme (FPTAS) for series-parallel graphs having exactly one supply vertex.