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| Natura: | Preprint |
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2023
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| Accesso online: | https://arxiv.org/abs/2310.11367 |
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| _version_ | 1866929282830303232 |
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| author | Chen, Yu Tan, Zihan |
| author_facet | Chen, Yu Tan, Zihan |
| contents | We study the following characterization problem. Given a set $T$ of terminals and a $(2^{|T|}-2)$-dimensional vector $π$ whose coordinates are indexed by proper subsets of $T$, is there a graph $G$ that contains $T$, such that for all subsets $\emptyset\subsetneq S\subsetneq T$, $π_S$ equals the value of the min-cut in $G$ separating $S$ from $T\setminus S$? The only known necessary conditions are submodularity and a special class of linear inequalities given by Chaudhuri, Subrahmanyam, Wagner and Zaroliagis.
Our main result is a new class of linear inequalities concerning laminar families, that generalize all previous ones. Using our new class of inequalities, we can generalize Karger's approximate min-cut counting result to graphs with terminals. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2310_11367 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Towards the Characterization of Terminal Cut Functions: a Condition for Laminar Families Chen, Yu Tan, Zihan Data Structures and Algorithms Discrete Mathematics Combinatorics We study the following characterization problem. Given a set $T$ of terminals and a $(2^{|T|}-2)$-dimensional vector $π$ whose coordinates are indexed by proper subsets of $T$, is there a graph $G$ that contains $T$, such that for all subsets $\emptyset\subsetneq S\subsetneq T$, $π_S$ equals the value of the min-cut in $G$ separating $S$ from $T\setminus S$? The only known necessary conditions are submodularity and a special class of linear inequalities given by Chaudhuri, Subrahmanyam, Wagner and Zaroliagis. Our main result is a new class of linear inequalities concerning laminar families, that generalize all previous ones. Using our new class of inequalities, we can generalize Karger's approximate min-cut counting result to graphs with terminals. |
| title | Towards the Characterization of Terminal Cut Functions: a Condition for Laminar Families |
| topic | Data Structures and Algorithms Discrete Mathematics Combinatorics |
| url | https://arxiv.org/abs/2310.11367 |