Minimum spanning tree with hop restrictions

  • Authors:

  • Refael Hassin;Asaf Levin

  • Affiliations:

  • Department of Statistics and Operations Research, Tel-Aviv University, Tel-Aviv 69978, Israel;Department of Statistics and Operations Research, Tel-Aviv University, Tel-Aviv 69978, Israel

  • Venue:
  • Journal of Algorithms - Special issue: Twelfth annual ACM-SIAM symposium on discrete algorithms
  • Year:
  • 2003

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Abstract

Let U = (uij)i,j=1n be a symmetric requirement matrix. Let d = (dij)i,j=1n be a cost metric. A spanning tree T = (V, ET) V = {1,2 ..... n} is feasible if for every pair of vertices v, w the v - w path in T contains at most uvw, edges. We explore the problem of finding a minimum cost feasible spanning tree, when uij ∈ {1,2, ∞}. We present a polynomial algorithm for the problem when the graph induced by the edges with uij