The complexity of approximating pspace-complete problems for hierarchical specifications

  • Authors:

  • Madhav V. Marathe;Harry B. Hunt, III;S. S. Ravi

  • Affiliations:

  • Department of Computer Science, University of Albany - State University of New York, Albany, NY;Department of Computer Science, University of Albany - State University of New York, Albany, NY;Department of Computer Science, University of Albany - State University of New York, Albany, NY

  • Venue:
  • Nordic Journal of Computing
  • Year:
  • 1994

Quantified Score

Hi-index 0.00

Visualization

Abstract

We extend the concept of polynomial time approximation algorithms to apply to problems for hierarchically specified graphs, many of which are PSPACE-complete. We present polynomial time approximation algorithms for several standard PSPACE-hard problems considered in the literature. In contrast, we prove that finding ε-approximations for any ε 0, for several other problems when the instances are specified hierarchically, is PSPACE-hard. We present polynomial time approximation algorithms for the following problems when the graphs are specified hierarchically: minimum vertex cover, maximum 3SAT, weighted max cut, minimum maximal matching, and bounded degree maximum independent set.In contrast, we show that for any ε 0, obtaining ε-approximations for the following problems when the instances are specified hierarchically is PSPACE-hard: the number of true gates in a monotone acyclic circuit when all input values are specified and the optimal value of the objective function of a linear program. It is also shown that obtaining a performance guarantee of less than 2 is PSPACE-hard for the following problems when the instances are specified hierarchically: high degree subgraph, k-vertex connected subgraph and k-edge connected subgraph.