DeepAI

# Minimum Weight Pairwise Distance Preservers

In this paper, we study the Minimum Weight Pairwise Distance Preservers (MWPDP) problem. Consider a positively weighted undirected/directed connected graph G = (V, E, c) and a subset P of pairs of vertices, also called demand pairs. A subgraph G' is a distance preserver with respect to P if and only if every pair (u, w) ∈ P satisfies dist_G' (u, w) = dist_G(u, w). In MWPDP problem, we aim to find the minimum-weight subgraph G^* that is a distance preserver with respect to P. Taking a shortest path between each pair in P gives us a trivial solution with the weight of at most U=∑_(u,v) ∈ P dist_G (u, w). Subsequently, we ask how much improvement we can make upon U. In other words, we opt to find a distance preserver G^* that maximizes U-c(G^*). Denote this problem as Cost Sharing Pairwise Distance Preservers (CSPDP), which has several applications in the planning and operations of transportation systems. The only known work that can provide a nontrivial solution for CSPDP is that of Chlamtáč et al. (SODA, 2017). This algorithm works for unweighted graphs and guarantees a non-zero objective only if the optimal solution is extremely sparse with respect to the trivial solution. We address this issue by proposing an O(|E|^1/2+ϵ)-approximation algorithm for CSPDP in weighted graphs that runs in O((|P||E|)^2.38 (1/ϵ)) time. Moreover, we prove CSPDP is at least as hard as LABEL-COVER_max. This implies that CSPDP cannot be approximated within O(|E|^1/6-ϵ) factor in polynomial time, unless there is an improvement in the notoriously difficult LABEL-COVER_max.

• 1 publication
• 3 publications
• 6 publications
03/17/2021

### On additive spanners in weighted graphs with local error

An additive +β spanner of a graph G is a subgraph which preserves distan...
10/01/2022

### An experimental study of algorithms for obtaining a singly connected subgraph

A directed graph G = (V,E) is singly connected if for any two vertice...
07/16/2022

### Envyfree Trip Planning in Group Trip Planning Query Problem

In recent times, Group Trip Planning Query (henceforth referred to as GT...
11/10/2020

### Adaptive Community Search in Dynamic Networks

Community search is a well-studied problem which, given a static graph a...
07/04/2018

### Near-Optimal Distance Emulator for Planar Graphs

Given a graph G and a set of terminals T, a distance emulator of G is an...
02/05/2019

### Network Resilience Assessment via QoS Degradation Metrics: An Algorithmic Approach

This paper focuses on network resilience to perturbation of edge weight....
07/25/2019

### Approximating APSP without Scaling: Equivalence of Approximate Min-Plus and Exact Min-Max

Zwick's (1+ε)-approximation algorithm for the All Pairs Shortest Path (A...