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Approximating the two-source minimum routing cost spanning trees Bang Ye Wu Shu-Te University.

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1 Approximating the two-source minimum routing cost spanning trees Bang Ye Wu Shu-Te University

2 Problem Definition Input: an undirected graph with nonnegative edge lengths, two vertices as sources and all vertices as destinations Output: a spanning tree such that the total distance from sources to destinations (including the sources) is minimum, that is, we want to minimize

3 Result The NP-hardness of the problem. A PTAS: for any  >0, the scheme finds a (1+  )-approximation solution with time complexity

4 Related problems OCT:  ij d T (i,j), arbitrary nonnegative requirements. MRCT: requirement=1 PROCT: ij =r i *r j, r i is nonnegative vertex weight SROCT: ij =r i +r j k-MRCT is a special case of SROCT. The sources have weight 1 and others have weight 0

5 OCT problems

6 Previous results problemApprox. ratioreference OCTO(lognloglogn)SICOMP PROCTPTASJALG SROCT2DAM MRCTPTASSICOMP

7 Future research k-MRCT, fixed k and arbitrary k K-OCT, fixed k and arbitrary k On the plane

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