Optimal Data Structures for Farthest-Point Queries in Cactus Networks

TL;DR

This paper develops optimal data structures for efficiently answering farthest-point and farthest-distance queries in complex network structures like trees, cycles, and cactus networks, enhancing computational geometry in network analysis.

Contribution

It introduces the first optimal data structures for farthest-point queries in cactus networks, extending previous work on simpler network types.

Findings

Optimal data structures for cactus networks

Efficient query support for farthest points and distances

Improved computational methods for network analysis

Abstract

Consider the continuum of points on the edges of a network, i.e., a connected, undirected graph with positive edge weights. We measure the distance between these points in terms of the weighted shortest path distance, called the network distance. Within this metric space, we study farthest points and farthest distances. We introduce optimal data structures supporting queries for the farthest distance and the farthest points on trees, cycles, uni-cyclic networks, and cactus networks.