Clustered Spanning Tree - Conditions for Feasibility
Let H =< V, S > be a hypergraph, where V is a set of vertices and S is a set of not necessarily disjoint clusters Si ⊆ V. The Clustered Spanning Tree problem is to find a spanning tree of G which satisfies that each cluster induces a subtree, when it exists. We provide an efficient and unique...
| Main Authors: | , , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
Discrete Mathematics & Theoretical Computer Science
2019-08-01
|
| Series: | Discrete Mathematics & Theoretical Computer Science |
| Subjects: | |
| Online Access: | https://dmtcs.episciences.org/4906/pdf |
| _version_ | 1797270030116716544 |
|---|---|
| author | Nili Guttmann-Beck Zeev Sorek Michal Stern |
| author_facet | Nili Guttmann-Beck Zeev Sorek Michal Stern |
| author_sort | Nili Guttmann-Beck |
| collection | DOAJ |
| description | Let H =< V, S > be a hypergraph, where V is a set of vertices and S is a set of not necessarily disjoint clusters Si ⊆ V. The Clustered Spanning Tree problem is to find a spanning tree of G which satisfies that each cluster induces a subtree, when it exists. We provide an efficient and unique algorithm which finds a feasible solution tree for H when it exists, or states that no feasible solution exists. The paper also uses special structures of the intersection graph of H to construct a feasible solution more efficiently. For cases when the hypergraph does not have a feasible solution tree, we consider adding vertices to exactly one cluster in order to gain feasibility. We characterize when such addition can gain feasibility, find the appropriate cluster and a possible set of vertices to be added. |
| first_indexed | 2024-04-25T01:57:47Z |
| format | Article |
| id | doaj.art-be4733a441ba454699f512bc9bd213a6 |
| institution | Directory Open Access Journal |
| issn | 1365-8050 |
| language | English |
| last_indexed | 2024-04-25T01:57:47Z |
| publishDate | 2019-08-01 |
| publisher | Discrete Mathematics & Theoretical Computer Science |
| record_format | Article |
| series | Discrete Mathematics & Theoretical Computer Science |
| spelling | doaj.art-be4733a441ba454699f512bc9bd213a62024-03-07T15:37:58ZengDiscrete Mathematics & Theoretical Computer ScienceDiscrete Mathematics & Theoretical Computer Science1365-80502019-08-01vol. 21 no. 1, ICGT 201810.23638/DMTCS-21-1-154906Clustered Spanning Tree - Conditions for FeasibilityNili Guttmann-BeckZeev SorekMichal Stern0Caesarea Rothschild Institute and Department of Computer ScienceLet H =< V, S > be a hypergraph, where V is a set of vertices and S is a set of not necessarily disjoint clusters Si ⊆ V. The Clustered Spanning Tree problem is to find a spanning tree of G which satisfies that each cluster induces a subtree, when it exists. We provide an efficient and unique algorithm which finds a feasible solution tree for H when it exists, or states that no feasible solution exists. The paper also uses special structures of the intersection graph of H to construct a feasible solution more efficiently. For cases when the hypergraph does not have a feasible solution tree, we consider adding vertices to exactly one cluster in order to gain feasibility. We characterize when such addition can gain feasibility, find the appropriate cluster and a possible set of vertices to be added.https://dmtcs.episciences.org/4906/pdf[info.info-dm]computer science [cs]/discrete mathematics [cs.dm] |
| spellingShingle | Nili Guttmann-Beck Zeev Sorek Michal Stern Clustered Spanning Tree - Conditions for Feasibility Discrete Mathematics & Theoretical Computer Science [info.info-dm]computer science [cs]/discrete mathematics [cs.dm] |
| title | Clustered Spanning Tree - Conditions for Feasibility |
| title_full | Clustered Spanning Tree - Conditions for Feasibility |
| title_fullStr | Clustered Spanning Tree - Conditions for Feasibility |
| title_full_unstemmed | Clustered Spanning Tree - Conditions for Feasibility |
| title_short | Clustered Spanning Tree - Conditions for Feasibility |
| title_sort | clustered spanning tree conditions for feasibility |
| topic | [info.info-dm]computer science [cs]/discrete mathematics [cs.dm] |
| url | https://dmtcs.episciences.org/4906/pdf |
| work_keys_str_mv | AT niliguttmannbeck clusteredspanningtreeconditionsforfeasibility AT zeevsorek clusteredspanningtreeconditionsforfeasibility AT michalstern clusteredspanningtreeconditionsforfeasibility |