A graph G =(V,E) is said to admit a system of μ collective additive tree r-spanners if there is a system (G) of at most μ spanning trees of G such that for any two vertices u,v of G a spanning tree (G) exists such that the distance in T between u and v is at most r plus their distance in G. In this paper, we examine the problem of finding "small" systems of collective additive tree r-spanners for small values of r on circle graphs and on polygonal graphs. Among other results, we show that every n-vertex circle graph admits a system of at most collective additive tree 2-spanners and every n-vertex k-polygonal graph admits a system of at most collective additive tree 2-spanners. Moreover, we show that every n-vertex k-polygonal graph admits an additive (k + 6)-spanner with at most 6n - 6 edges and every n-vertex 3-polygonal graph admits a system of at most 3 collective additive tree 2-spanners and an additive tree 6-spanner. All our collective tree spanners as well as all sparse spanners are constructible in polynomial time. © 2008 Springer Berlin Heidelberg.
CITATION STYLE
Dragan, F. F., Corneil, D. G., Köhler, E., & Xiang, Y. (2008). Additive spanners for circle graphs and polygonal graphs. In Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) (Vol. 5344 LNCS, pp. 110–121). https://doi.org/10.1007/978-3-540-92248-3_11
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