Yusuke Kobayashi gave an online talk on his algorithm for finding a large subgraph keeping the distance function differs by at most a constant at the Virtual Discrete Math Colloquium

On January 20, 2021, Yusuke Kobayashi (小林 佑輔) from RIMS, Kyoto University gave an online talk at the Virtual Discrete Math Colloquium on the fixed-parameter tractability of the problem of finding a small set X of edges such that for every pair v, w of vertices the distance from v to w in G is at most a constant plus the distance from v to w in G-X. The title of his talk was “An FPT Algorithm for Minimum Additive Spanner Problem“.

Yusuke Kobayashi (小林 佑輔), An FPT Algorithm for Minimum Additive Spanner Problem

For a positive integer t and a graph G, an additive t-spanner of G is a spanning subgraph in which the distance between every pair of vertices is at most the original distance plus t. Minimum Additive t-Spanner Problem is to find an additive t-spanner with the minimum number of edges in a given graph, which is known to be NP-hard. Since we need to care about global properties of graphs when we deal with additive t-spanners, Minimum Additive t-Spanner Problem is hard to handle, and hence only few results are known for it. In this talk, we study Minimum Additive t-Spanner Problem from the viewpoint of parameterized complexity. We formulate a parameterized version of the problem in which the number of removed edges is regarded as a parameter, and give a fixed-parameter algorithm for it. We also extend our result to (α,β)-spanners.