Minimizing the total weighted pairwise connection time in network construction problems

TL;DR

This paper addresses an NP-hard network construction problem, proposing polynomial algorithms for special cases like trees with few leaves and networks with limited relevant pairs to optimize connection times.

Contribution

It introduces polynomial algorithms for the problem on trees with few leaves and on networks with limited relevant pairs, advancing solutions for specific network structures.

Findings

Polynomial algorithms for trees with a fixed number of leaves.

Polynomial algorithms for general networks with a fixed number of relevant pairs.

The problem remains NP-hard in general, but tractable in these special cases.

Abstract

It is required to find an optimal order of constructing the edges of a network so as to minimize the sum of the weighted connection times of relevant pairs of vertices. Construction can be performed anytime anywhere in the network, with a fixed overall construction speed. The problem is strongly NP-hard even on stars. We present polynomial algorithms for the problem on trees with a fixed number of leaves, and on general networks with a fixed number of relevant pairs.