Network installation and recovery: approximation lower bounds and faster exact formulations

TL;DR

This paper investigates the computational complexity of the Neighbor Aided Network Installation Problem (NANIP), establishes hardness and approximation bounds, and introduces a more efficient integer programming formulation for practical solving.

Contribution

It provides the first hardness results for NANIP with convex decreasing costs, derives approximation bounds for greedy algorithms, and proposes an improved integer programming approach.

Findings

NANIP is NP-hard even with convex decreasing cost functions.

A linear approximation lower bound for greedy algorithms is established.

A new integer programming formulation significantly speeds up solving NANIP.

Abstract

We study the Neighbor Aided Network Installation Problem (NANIP) introduced previously which asks for a minimal cost ordering of the vertices of a graph, where the cost of visiting a node is a function of the number of neighbors that have already been visited. This problem has applications in resource management and disaster recovery. In this paper we analyze the computational hardness of NANIP. In particular we show that this problem is NP-hard even when restricted to convex decreasing cost functions, give a linear approximation lower bound for the greedy algorithm, and prove a general sub-constant approximation lower bound. Then we give a new integer programming formulation of NANIP and empirically observe its speedup over the original integer program.