Approximating the two-source minimum routing cost spanning trees

Bang Ye WuShu-Te University

Problem Definition

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

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Result

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

Related problems

OCT: ijdT(i,j), arbitrary nonnegative requirements.MRCT: requirement=1PROCT: ij=ri*rj, ri is nonnegative vertex weightSROCT: ij=ri+rj

k-MRCT is a special case of SROCT. The sources have weight 1 and others have weight 0

OCT problemsm

ore

gene

ral

p-source MRCT, arbitrary p

2-source MRCT

Optimum Communication spanning Tree

SROCTPROCT

MRCT p-source MRCT, fixed p

2-source OCT

p-source OCT, fixed p

Previous results

problem Approx. ratio reference

OCT O(lognloglogn) SICOMP

PROCT PTAS JALG

SROCT 2 DAM

MRCT PTAS SICOMP

Future research

k-MRCT, fixed k and arbitrary kK-OCT, fixed k and arbitrary kOn the plane