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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.
@article{RO_2014__48_1_25_0,
author = {Szachniuk, Marta and Cristina De Cola, Maria and Felici, Giovanni and Blazewicz, Jacek},
title = {The {Orderly} {Colored} {Longest} {Path} {Problem} - a survey of applications and new algorithms},
journal = {RAIRO - Operations Research - Recherche Op\'erationnelle},
pages = {25--51},
publisher = {EDP-Sciences},
volume = {48},
number = {1},
year = {2014},
doi = {10.1051/ro/2013046},
mrnumber = {3143767},
zbl = {1288.90117},
language = {en},
url = {http://geodesic.mathdoc.fr/articles/10.1051/ro/2013046/}
}
TY - JOUR AU - Szachniuk, Marta AU - Cristina De Cola, Maria AU - Felici, Giovanni AU - Blazewicz, Jacek TI - The Orderly Colored Longest Path Problem - a survey of applications and new algorithms JO - RAIRO - Operations Research - Recherche Opérationnelle PY - 2014 SP - 25 EP - 51 VL - 48 IS - 1 PB - EDP-Sciences UR - http://geodesic.mathdoc.fr/articles/10.1051/ro/2013046/ DO - 10.1051/ro/2013046 LA - en ID - RO_2014__48_1_25_0 ER -
%0 Journal Article %A Szachniuk, Marta %A Cristina De Cola, Maria %A Felici, Giovanni %A Blazewicz, Jacek %T The Orderly Colored Longest Path Problem - a survey of applications and new algorithms %J RAIRO - Operations Research - Recherche Opérationnelle %D 2014 %P 25-51 %V 48 %N 1 %I EDP-Sciences %U http://geodesic.mathdoc.fr/articles/10.1051/ro/2013046/ %R 10.1051/ro/2013046 %G en %F RO_2014__48_1_25_0
Szachniuk, Marta; Cristina De Cola, Maria; Felici, Giovanni; Blazewicz, Jacek. The Orderly Colored Longest Path Problem - a survey of applications and new algorithms. RAIRO - Operations Research - Recherche Opérationnelle, Tome 48 (2014) no. 1, pp. 25-51. doi: 10.1051/ro/2013046
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