Most Balanced Minimum Cuts and Partially Ordered Knapsack
| dc.contributor.author | Bonsma, Paul | |
| dc.date.accessioned | 2021-12-17T10:07:19Z | |
| dc.date.available | 2021-12-17T10:07:19Z | |
| dc.date.issued | 2007 | |
| dc.description.abstract | We consider the problem of finding most balanced cuts among minimum st-edge cuts and minimum st-vertex cuts, for given vertices s and t, according to different balance criteria. For edge cuts [S,V(G)-S] we seek to maximize min{|S|,|V(G)-S|}. For vertex cuts C of G we consider the objectives of (i) maximizing min{|S|,|T|}, where {S,T} is a partition of V(G)-C with s in S, t in T and [S,T] empty, (ii) minimizing the order of the largest component of G-C, and (iii) maximizing the order of the smallest component of G-C. All of these problems are shown to be NP-hard. We give a PTAS for the edge cut variant and for (i). We give a 2-approximation for (ii), and show that no non-trivial approximation exists for (iii) unless P=NP. To prove these results we show that we can partition the vertices of G, and define a partial order on the subsets of the partition, such that ideals of the partial order correspond bijectively to minimum st-cuts of G. This shows that the problems are closely related to Uniform Partially Ordered Knapsack (UPOK), a variant of POK where element utilities are equal to element weights. Our PTAS is also a PTAS for special types of UPOK instances. | en |
| dc.identifier.issn | 2197-8085 | |
| dc.identifier.uri | https://depositonce.tu-berlin.de/handle/11303/15609 | |
| dc.identifier.uri | http://dx.doi.org/10.14279/depositonce-14382 | |
| dc.language.iso | en | en |
| dc.rights.uri | http://rightsstatements.org/vocab/InC/1.0/ | en |
| dc.subject.ddc | 510 Mathematik | en |
| dc.subject.other | Balanced Cuts | en |
| dc.subject.other | Partially Ordered Knapsack | en |
| dc.subject.other | Approximation Algorithms | en |
| dc.title | Most Balanced Minimum Cuts and Partially Ordered Knapsack | en |
| dc.type | Research Paper | en |
| dc.type.version | submittedVersion | en |
| tub.accessrights.dnb | free | en |
| tub.affiliation | Fak. 2 Mathematik und Naturwissenschaften::Inst. Mathematik | de |
| tub.affiliation.faculty | Fak. 2 Mathematik und Naturwissenschaften | de |
| tub.affiliation.institute | Inst. Mathematik | de |
| tub.publisher.universityorinstitution | Technische Universität Berlin | en |
| tub.series.issuenumber | 2007, 43 | en |
| tub.series.name | Preprint-Reihe des Instituts für Mathematik, Technische Universität Berlin | en |
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