Search results for "Symmetry reduction"
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A note on symmetry reduction for circular traveling tournament problems
2011
Abstract The traveling tournament problem (TTP) consists of finding a distance-minimal double round-robin tournament where the number of consecutive breaks is bounded. Easton et al. (2001) introduced the so-called circular TTP instances, where venues of teams are located on a circle. The distance between neighboring venues is one, so that the distance between any pair of teams is the distance on the circle. It is empirically proved that these instances are very hard to solve due to the inherent symmetry. This note presents new ideas to cut off essentially identical parts of the solution space. Enumerative solution approaches, e.g. relying on branch-and-bound, benefit from this reduction. We…
Symmetry reduction of a model in spherical symmetry for benign tumor
2004
A PDEs system, describing the expansive growth of a benign tumor and the phe- nomenon of encapsulation, is studied via a group analysis approach. A weak equiv- alence classi¯cation is obtained and the original PDEs system is reduced to an ODEs system. Numerical simulations are performed both for ODEs and PDEs, which turn out to be in perfect agreement between each other, showing a realistic enough description of the biological process.