- Published 2008 in CPM

Let G be an unweighted and undirected graph of n nodes, and let D be the n × n matrix storing the All-Pairs-Shortest-Path distances in G. Since D contains integers in [n]∪+∞, its plain storage takes n log(n+1) bits. However, a simple counting argument shows that n/2 bits are necessary to store D. In this paper we investigate the question of finding a succinct representation of D that requires O(n) bits of storage and still supports constant-time access to each of its entries. This is asymptotically optimal in the worst case, and far from the informationtheoretic lower-bound by a multiplicative factor log2 3 ≃ 1.585. As a result O(1) bits per pairs of nodes in G are enough to retain constanttime access to their shortest-path distance. We achieve this result by reducing the storage of D to the succinct storage of labeled trees and ternary sequences, for which we properly adapt and orchestrate the use of known compressed data structures.

@inproceedings{Nitto2008OnCR,
title={On Compact Representations of All-Pairs-Shortest-Path-Distance Matrices},
author={Igor Nitto and Rossano Venturini},
booktitle={CPM},
year={2008}
}