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## Approximating the two-source minimum routing cost spanning trees

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**Approximating the two-source minimum routing cost spanning**trees Bang Ye Wu Shu-Te University**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**Result**• The NP-hardness of the problem. • A PTAS: for any e>0, the scheme finds a (1+ e)-approximation solution with time complexity**Related problems**• OCT: SlijdT(i,j), arbitrary nonnegative requirements. • MRCT: requirement=1 • PROCT: lij=ri*rj, ri is nonnegative vertex weight • SROCT: lij=ri+rj • k-MRCT is a special case of SROCT. The sources have weight 1 and others have weight 0**Future research**• k-MRCT, fixed k and arbitrary k • K-OCT, fixed k and arbitrary k • On the plane