eng
Schloss Dagstuhl – Leibniz-Zentrum für Informatik
Leibniz International Proceedings in Informatics
1868-8969
2022-12-14
7:1
7:15
10.4230/LIPIcs.ISAAC.2022.7
article
Approximating the Minimum Logarithmic Arrangement Problem
Mestre, Julián
1
2
https://orcid.org/0000-0003-4948-2998
Pupyrev, Sergey
1
https://orcid.org/0000-0003-4089-673X
Meta Platforms Inc., USA
School of Computer Science, The University of Sydney, Australia
We study a graph reordering problem motivated by compressing massive graphs such as social networks and inverted indexes. Given a graph, G = (V, E), the Minimum Logarithmic Arrangement problem is to find a permutation, π, of the vertices that minimizes ∑_{(u, v) ∈ E} (1 + ⌊ lg |π(u) - π(v)| ⌋).
This objective has been shown to be a good measure of how many bits are needed to encode the graph if the adjacency list of each vertex is encoded using relative positions of two consecutive neighbors under the π order in the list rather than using absolute indices or node identifiers, which requires at least lg n bits per edge.
We show the first non-trivial approximation factor for this problem by giving a polynomial time 𝒪(log k)-approximation algorithm for graphs with treewidth k.
https://drops.dagstuhl.de/storage/00lipics/lipics-vol248-isaac2022/LIPIcs.ISAAC.2022.7/LIPIcs.ISAAC.2022.7.pdf
approximation algorithms
graph compression