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2012, with author Felici G., in the category IASI Research Reports
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IASI Research Report n. 12-29 De Cola C,

Giovanni Felici,

Szachniuk M.The Orderly Colored Longest Path ProblemABSTRACT We consider the problem of finding a longest path in a graph whose edges are colored with c colors, under the constraint that the edges of the path follow a given order of colors. The problem is referred to as the Orderly Colored Longest Path on a c-edge colored graph (OCLP). We show its relations with similar problems already studied and consider three alternative integer programming models for this problem.
The three models are formulated by means of max flow problems on a directed graph with packing constraints over certain partitions of the nodes. This problem has not been modeled and studied in previous literature. A recent and relevant application is related with the interpretation of Nuclear Magnetic Resonance experiments. Besides, applications can be found in transportation, games, and grid graphs. The interestingness of this problem is motivated by the fact that it models the relations of consecutive edges of the path. All three integer programming formulations have been implemented and compared on a set of randomly generated instances.