Inapproximability of Orthogonal Compaction

TL;DR

This paper proves that approximating orthogonal graph drawing compaction problems within any polynomial factor is NP-hard, and introduces a fixed-parameter algorithm for small-row compaction testing.

Contribution

It establishes inapproximability bounds for multiple orthogonal graph drawing compaction problems and presents a fixed-parameter algorithm for small-row solutions.

Findings

Orthogonal compaction problems are hard to approximate within polynomial factors.

A fixed-parameter-tractable algorithm is provided for testing small-row compactability.

Certain optimization goals in orthogonal graph drawing cannot be efficiently approximated.

Abstract

We show that several problems of compacting orthogonal graph drawings to use the minimum number of rows, area, length of longest edge or total edge length cannot be approximated better than within a polynomial factor of optimal in polynomial time unless P = NP. We also provide a fixed-parameter-tractable algorithm for testing whether a drawing can be compacted to a small number of rows.