Tractable Parameterizations for the Minimum Linear Arrangement Problem

Abstract

Abstract. The Minimum Linear Arrangement (MLA) problem asks to embed a given graph on the integer line so that the sum of the edge lengths of the embedded graph is minimized. Most layout problems are either intractable, or not known to be tractable, parameterized by the treewidth of the input graphs. We investigate MLA with respect to three parameters that provide more structure than treewidth. In particular, we give a factor (1 + ε)-approximation algorithm for MLA parameterized by (ε, k), where k is the vertex cover number of the input graph. By a similar approach, we describe two FPT algorithms that exactly solve MLA parameterized by, respectively, the max-leaf and edge-clique-cover numbers of the input graph.

Ordering a Sparse Graph to Minimize the Sum of Right Ends of Edges

“…The minimum linear arrangement problem is a classic NP-complete problem [12] and has been intensively studied. Approximation algorithms and inapproximability results are known [1,2,8,14], as well as exact exponential and parameterized algorithms [3,[9][10][11], and efficient algorithms for special graph classes [5][6][7]13]. MinSumEnds is much less explored.…”