The orderly colored longest path problem - A survey of applications and new algorithms

Marta Szachniuk, Maria Cristina De Cola, Giovanni Felici, Jacek Blazewicz

Research output: Contribution to journalArticlepeer-review

Abstract

A concept of an Orderly Colored Longest Path (OCLP) refers to the problem of finding the longest path in a graph whose edges are colored with a given number of colors, under the constraint that the path follows a predefined order of colors. The problem has not been widely studied in the previous literature, especially for more than two colors in the color arrangement sequence. The recent and relevant application of OCLP is related to the interpretation of Nuclear Magnetic Resonance experiments for RNA molecules. Besides, an employment of this specific graph model can be found in transportation, games, and grid graphs. OCLP models the relationships between consecutive edges of the path, thus it appears very useful in representing the real problems with specific ties between their components. In the paper, we show OCLP's correlation with similar issues known in graph theory. We describe the applications, three alternative models and new integer programming algorithms to solve OCLP. They are formulated by means of max flow problems in a directed graph with packing constraints over certain partitions of nodes. The methods are compared in a computational experiment run for a set of randomly generated instances.

Original languageEnglish
Pages (from-to)25-51
Number of pages27
JournalRAIRO - Operations Research
Volume48
Issue number1
DOIs
Publication statusPublished - Jan 2014

Keywords

  • Alternating path
  • Edge colored graph
  • Longest path problem

ASJC Scopus subject areas

  • Management Science and Operations Research
  • Theoretical Computer Science
  • Computer Science Applications

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