TY  - INPR
A1  - Bunke, Florentine
A1  - Hamacher, Horst W.
A1  - Maffioli, Francesco
A1  - Schwahn, Anne
T1  - Minimum Cut Bases in Undirected Networks
N2  - Given an undirected, connected network G = (V,E) with weights on the edges, the cut basis problem is asking for a maximal number of linear independent cuts such that the sum of the cut weights is minimized. Surprisingly, this problem has not attained as much attention as its graph theoretic counterpart, the cycle basis problem. We consider two versions of the problem, the unconstrained and the fundamental cut basis problem. For the unconstrained case, where the cuts in the basis can be of an arbitrary kind, the problem can be written as a multiterminal network flow problem and is thus solvable in strongly polynomial time. The complexity of this algorithm improves the complexity of the best algorithms for the cycle basis problem, such that it is preferable for cycle basis problems in planar graphs. In contrast, the fundamental cut basis problem, where all cuts in the basis are obtained by deleting an edge, each, from a spanning tree T is shown to be NP-hard. We present heuristics, integer programming formulations and summarize first experiences with numerical tests.
T3  - Report in Wirtschaftsmathematik (WIMA Report) - 108 
KW  - cut basis problem
KW  - graph and network algorithm
KW  - integer programming
Y1  - 2007
UR  - https://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/1857
UR  - https://nbn-resolving.org/urn:nbn:de:hbz:386-kluedo-14913
ER  -