A probabilistic algorithm for Optimal Linear Arrangements

Berend, D.

doi:10.1016/j.dam.2026.05.001

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A probabilistic algorithm for Optimal Linear Arrangements

2026-10-15

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Berend, D.

Mamana, S. *

DOI：10.1016/j.dam.2026.05.001

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Abstract

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The Optimal Linear Arrangement (OLA) problem seeks a vertex ordering of a graph that minimizes the sum of edge lengths, a fundamental challenge in graph layout, with applications in VLSI design, network optimization, and data visualization. We propose a basic randomized algorithm and enhance it using the method of conditional expectations to derive a deterministic algorithm with guaranteed performance bounds. Our theoretical analysis includes a concentration result showing that for random graphs, the optimal OLA value concentrates around the expected value of a random arrangement. Additionally, we extend the problem to weighted graphs and demonstrate the effectiveness of our algorithms through empirical evaluations. (c) 2026 Elsevier B.V. All rights are reserved, including those for text and data mining, AI training, and similar technologies.

Keywords:

Linear arrangement

Graph

Random graph

Derandomization

Integer linear programming

Method of conditional expectations