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The Fan-Raspaud conjecture: A randomized algorithmic approach and application to the pair assignment problem in cubic networks

100%
Formanowicz P., Tanaś K.
International Journal of Applied Mathematics and Computer Science
|
2012
|
tom 22
|
nr 3
765-778
EN
It was conjectured by Fan and Raspaud (1994) that every bridgeless cubic graph contains three perfect matchings such that every edge belongs to at most two of them. We show a randomized algorithmic way of finding Fan-Raspaud colorings of a given cubic graph and, analyzing the computer results, we try to find and describe the Fan-Raspaud colorings for some selected classes of cubic graphs. The presented algorithms can then be applied to the pair assignment problem in cubic computer networks. Another possible application of the algorithms is that of being a tool for mathematicians working in the field of cubic graph theory, for discovering edge colorings with certain mathematical properties and formulating new conjectures related to the Fan-Raspaud conjecture.
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Some remarks on evaluating the quality of the multiple sequence alignment based on the BALiBASE benchmark

81%
Błażewicz J., Formanowicz P., Wojciechowski P.
International Journal of Applied Mathematics and Computer Science
|
2009
|
tom 19
|
nr 4
675-678
EN
BAliBASE is one of the most widely used benchmarks for multiple sequence alignment programs. The accuracy of alignment methods is measured by bali score-an application provided together with the database. The standard accuracy measures are the Sum of Pairs (SP) and the Total Column (TC). We have found that, for non-core block columns, results calculated by bali score are different from those obtained on the basis of the formal definitions of the measures. We do not claim that one of these measures is better than the other, but they are definitely different. Such a situation can be the source of confusion when alignments obtained using various methods are compared. Therefore, we propose a new nomenclature for the measures of the quality of multiple sequence alignments to distinguish which one was actually calculated. Moreover, we have found that the occurrence of a gap in some column in the first sequence of the reference alignment causes column discarding.
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