Ordering a sparse graph to minimize the sum of right ends of edges
Paper in proceedings, 2020

Motivated by a warehouse logistics problem we study mappings of the vertices of a graph onto prescribed points on the real line that minimize the sum (or equivalently, the average) of the coordinates of the right ends of all edges. We focus on graphs whose edge numbers do not exceed the vertex numbers too much, that is, graphs with few cycles. Intuitively, dense subgraphs should be placed early in the ordering, in order to finish many edges soon. However, our main “calculation trick” is to compare the objective function with the case when (almost) every vertex is the right end of exactly one edge. The deviations from this case are described by “charges” that can form “dipoles”. This reformulation enables us to derive polynomial algorithms and NP-completeness results for relevant special cases, and FPT results.

Cycle

3-core

Minimum linear arrangement

pick-by-order

Elimination ordering

Tree

2-core

Dynamic programming on subsets

Author

Peter Damaschke

Chalmers, Computer Science and Engineering (Chalmers), Data Science

Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

03029743 (ISSN) 16113349 (eISSN)

Vol. 12126 224-236

31st International Workshop on Combinatorial Algorithms IWOCA 2020
Bordeaux, France,

Roots

Basic sciences

Subject Categories

Computer Science

DOI

10.1007/978-3-030-48966-3_17

More information

Latest update

8/12/2020