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- W1995818744 abstract "In this paper we introduce a new vector space associated with the paths and cycles in a graph (this space properly includes the well-known cycle space). We present a polynomial algorithm for finding a minimum weight basis for this space; we then present an application of this algorithm. The application is an algorithm that finds in a graph a minimum weight subgraph whose cycle space has specified dimension k (when k = 1, this is the problem of finding a minimum weight cycle in a graph). We then show how this algorithm easily provides a new algorithm for the planar k-split problem; for a planar graph, this is the problem of finding a minimum weight set of edges whose deletion results in a graph with k components (when k = 2, this is the problem of finding a minimum cut in a planar graph). The algorithm for the application is polynomial for fixed k. In particular, for the planar three-split problem, our algorithm can be implemented with worst case time complexity O(|V|3), whereas the best previous algorithm has complexity O(|V|6 log|V|)." @default.
- W1995818744 created "2016-06-24" @default.
- W1995818744 creator A5079559219 @default.
- W1995818744 date "1993-07-01" @default.
- W1995818744 modified "2023-09-27" @default.
- W1995818744 title "Minimum Path Bases" @default.
- W1995818744 doi "https://doi.org/10.1006/jagm.1993.1033" @default.
- W1995818744 hasPublicationYear "1993" @default.
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