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• W2952613191 abstract "Using the framework of advice complexity, we study the amount of knowledge about the future that an online algorithm needs to color the edges of a graph optimally, i.e., using as few colors as possible. For graphs of maximum degree $Delta$, it follows from Vizing's Theorem that $O(mlog Delta)$ bits of advice suffice to achieve optimality, where $m$ is the number of edges. We show that for graphs of bounded degeneracy (a class of graphs including e.g. trees and planar graphs), only $O(m)$ bits of advice are needed to compute an optimal solution online, independently of how large $Delta$ is. On the other hand, we show that $Omega (m)$ bits of advice are necessary just to achieve a competitive ratio better than that of the best deterministic online algorithm without advice. Furthermore, we consider algorithms which use a fixed number of advice bits per edge (our algorithm for graphs of bounded degeneracy belongs to this class of algorithms). We show that for bipartite graphs, any such algorithm must use at least $Omega(mlog Delta)$ bits of advice to achieve optimality." @default.
• W2952613191 created "2019-06-27" @default.
• W2952613191 creator A5027425067 @default.
• W2952613191 date "2014-10-29" @default.
• W2952613191 modified "2023-09-27" @default.
• W2952613191 title "Optimal Online Edge Coloring of Planar Graphs with Advice" @default.
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• W2952613191 hasPublicationYear "2014" @default.
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