Combinatorial Optimization with Explicit Delineation of the Ground Set by a Collection of Subsets

  title={Combinatorial Optimization with Explicit Delineation of the Ground Set by a Collection of Subsets},
  author={M. Dror and J. Orlin},
  journal={SIAM J. Discret. Math.},
  • M. Dror, J. Orlin
  • Published 2008
  • Mathematics, Computer Science
  • SIAM J. Discret. Math.
  • We examine a selective list of combinatorial optimization problems in NP with respect to inapproximability (Arora and Lund (1997)) given that the ground set of elements $N$ has additional characteristics. For each problem in this paper, the set $N$ is expressed explicitly by subsets of $N$ either as a partition or in the form of a cover. The problems examined are generalizations of well-known classical graph problems and include the minimal spanning tree problem, a number of elementary machine… CONTINUE READING
    15 Citations
    A PTAS for Euclidean TSP with Hyperplane Neighborhoods
    • 4
    • PDF
    A QPTAS for TSP with Fat Weakly Disjoint Neighborhoods in Doubling Metrics
    • 6
    • PDF
    A QPTAS for TSP with fat weakly disjoint neighborhoods in doubling metrics
    • 21
    • PDF
    Complexity and approximability of the Euclidean generalized traveling salesman problem in grid clusters
    A PTAS for TSP with neighborhoods among fat regions in the plane
    • 87
    • PDF
    Constant-Factor Approximation for TSP with Disks
    • 10
    • PDF
    The Traveling Salesman Problem for Lines, Balls, and Planes
    • 13
    • PDF
    A constant-factor approximation algorithm for TSP with pairwise-disjoint connected neighborhoods in the plane
    • 42
    • PDF


    Generalized Steiner Problems and Other Variants
    • 34
    On the Complexity of Approximating TSP with Neighborhoods and Related Problems
    • 34
    When Hamming Meets Euclid: The Approximability of Geometric TSP and Steiner Tree
    • L. Trevisan
    • Computer Science, Mathematics
    • SIAM J. Comput.
    • 2000
    • 44
    • PDF
    The Budgeted Maximum Coverage Problem
    • 779
    • PDF
    Approximation Algorithms for the Geometric Covering Salesman Problem
    • 288
    Worst-Case Analysis of a New Heuristic for the Travelling Salesman Problem
    • 1,325
    Some NP-complete geometric problems
    • 369
    • Highly Influential
    • PDF
    The generalized minimum spanning tree problem
    • P. Pop
    • Mathematics, Chemistry
    • 2000
    • 90
    • PDF
    On the generalized minimum spanning tree problem
    • 101
    Approximate Solution of NP Optimization Problems
    • 115
    • PDF