A certifying and dynamic algorithm for the recognition of proper circular-arc graphs
We present a dynamic algorithm for the recognition of proper circular-arc (PCA) graphs, that supports the insertion and removal of vertices (together with its incident edges). The main feature of the algorithm is that it outputs a minimally non-PCA induced subgraph when the insertion of a vertex fai...
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| Format: | article |
| Status: | Published version |
| Publication Date: | 2021 |
| Country: | Argentina |
| Institution: | Consejo Nacional de Investigaciones Científicas y Técnicas |
| Repository: | CONICET Digital (CONICET) |
| Language: | English |
| OAI Identifier: | oai:ri.conicet.gov.ar:11336/173301 |
| Online Access: | http://hdl.handle.net/11336/173301 |
| Access Level: | Open access |
| Keyword: | CERTIFYING ALGORITHM DYNAMIC REPRESENTATION PROPER CIRCULAR-ARC GRAPHS PROPER HELLY CIRCULAR-ARC GRAPHS PROPER INTERVAL GRAPH https://purl.org/becyt/ford/1.2 https://purl.org/becyt/ford/1 |
| Summary: | We present a dynamic algorithm for the recognition of proper circular-arc (PCA) graphs, that supports the insertion and removal of vertices (together with its incident edges). The main feature of the algorithm is that it outputs a minimally non-PCA induced subgraph when the insertion of a vertex fails. Each operation cost O(logn+d) time, where n is the number vertices and d is the degree of the modified vertex. When removals are disallowed, each insertion is processed in O(d) time. The algorithm also provides two constant-time operations to query if the dynamic graph is proper Helly (PHCA) or proper interval (PIG). When the dynamic graph is not PHCA (resp. PIG), a minimally non-PHCA (resp. non-PIG) induced subgraph is obtained. |
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