TY - GEN

T1 - Approximating the minimum degree spanning tree to within one from the optimal degree

AU - Fürer, Martin

AU - Raghavachari, Balaji

PY - 1992/9/1

Y1 - 1992/9/1

N2 - We consider the problem of constructing a spanning tree for a graph G = (V, E) with n vertices whose maximal degree is the smallest among all spanning trees of G. This problem is easily shown to be NP-haxd. We describe an iterative polynomial time approximation algorithm for this problem. This algorithm computes a spanning tree whose maximal degree is at most O(Delta;z.ast; +log n), where Δz.ast; is the degree of some optimal tree. The result is generalized to the case where only some vertices need to be connected (Steiner case) and to the case of directed graphs. It is then shown that our algorithm can be refined to produce a spanning tree of degree at most Δz.st; + 1. Unless P = NP, this is the best bound achievable in polynomial time.

AB - We consider the problem of constructing a spanning tree for a graph G = (V, E) with n vertices whose maximal degree is the smallest among all spanning trees of G. This problem is easily shown to be NP-haxd. We describe an iterative polynomial time approximation algorithm for this problem. This algorithm computes a spanning tree whose maximal degree is at most O(Delta;z.ast; +log n), where Δz.ast; is the degree of some optimal tree. The result is generalized to the case where only some vertices need to be connected (Steiner case) and to the case of directed graphs. It is then shown that our algorithm can be refined to produce a spanning tree of degree at most Δz.st; + 1. Unless P = NP, this is the best bound achievable in polynomial time.

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M3 - Conference contribution

AN - SCOPUS:85026575220

T3 - Proceedings of the Annual ACM-SIAM Symposium on Discrete Algorithms

SP - 317

EP - 324

BT - Proceedings of the 3rd Annual ACM-SIAM Symposium on Discrete Algorithms. SODA 1992

PB - Association for Computing Machinery

T2 - 3rd Annual ACM-SIAM Symposium on Discrete Algorithms. SODA 1992

Y2 - 27 January 1992 through 29 January 1992

ER -