Establishing Multiple Survivable Connections (Extended Version)

TL;DR

This paper investigates the complexity of establishing multiple survivable network connections, identifying tractable cases with polynomial solutions and proposing heuristics for NP-hard variants, supported by simulations.

Contribution

It provides a comprehensive complexity analysis of multi-connection survivable network establishment and introduces heuristics for NP-hard cases, extending results to fixed and variable numbers of connections.

Findings

Only one variant of two-connection problem is tractable with polynomial solutions.

Heuristics outperform straightforward methods in simulations.

Problems with fixed number of connections are tractable; others are NP-hard.

Abstract

We consider the establishment of connections in survivable networks, where each connection is allocated with a working (primary) path and a protection (backup) path. While many optimal solutions have been found for the establishment of a single connection, only heuristics have been proposed for the multi-connection case. We investigate the algorithmic tractability of multi-connection establishment problems, both in online and offline frameworks. First, we focus on the special case of two connections, and study the tractability of three variants of the problem. We show that only one variant is tractable, for which we establish an optimal solution of polynomial complexity. For the other variants, which are shown to be NP-hard, heuristic schemes are proposed. These heuristics are designed based on the insight gained from our study. Through simulations, we indicate the advantages of these heuristics over more straightforward alternatives. We extend our study to K connections, for a fixed K that is larger than 2. We prove the tractability of online and offline variants of the problem, in which sharing links along backup paths is allowed, and we establish corresponding optimal solutions. On the other hand, we show that, if the number of connections is not fixed (i.e., K is not O(1)), then the problem is, in general, NP-hard.