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An FPTAS for Connectivity Interdiction.

Chien-Chung Huang1, Nidia Obscura Acosta2, Sorrachai Yingchareonthawornchai3

  • 1Department of Computer Science, École Normale Supérieure, Paris, France.

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Summary
This summary is machine-generated.

This study provides a fully polynomial-time approximation scheme (FPTAS) for the connectivity interdiction problem. Faster exact and approximation algorithms are also developed for unit edge costs, advancing graph cut research.

Keywords:
Approximation AlgorithmsCombinatorial Optimization

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Area of Science:

  • Graph Theory
  • Combinatorial Optimization
  • Computer Science

Background:

  • The connectivity interdiction problem involves minimizing remaining edge weights after removing edges under a budget.
  • This NP-hard problem is a generalization of the knapsack problem.
  • Prior work established a polynomial-time approximation scheme (PTAS) and exact algorithms for unit edge costs.

Purpose of the Study:

  • To determine if a fully polynomial-time approximation scheme (FPTAS) is achievable for the general connectivity interdiction problem.
  • To develop faster exact and approximation algorithms for the special case of unit edge costs.

Main Methods:

  • Establishing a connection to a novel intermediate problem: the normalized min-cut.
  • The normalized min-cut problem penalizes remaining edge weights based on the number of edges removed for free.

Main Results:

  • An affirmative answer to the existence of an FPTAS for the general connectivity interdiction problem.
  • Development of improved exact and approximation algorithms for the unit edge cost variant.

Conclusions:

  • The FPTAS for the connectivity interdiction problem is now established.
  • The normalized min-cut provides a key technical advancement for solving related graph cut problems.