Low congestion online routing and an improved mistake bound for online prediction of graph labeling
Clinical Orthopaedics and Related Research(2008)
摘要
In this paper, we show a connection between a certain online low-congestion
routing problem and an online prediction of graph labeling. More specifically,
we prove that if there exists a routing scheme that guarantees a congestion of
$\alpha$ on any edge, there exists an online prediction algorithm with mistake
bound $\alpha$ times the cut size, which is the size of the cut induced by the
label partitioning of graph vertices. With previous known bound of $O(\log n)$
for $\alpha$ for the routing problem on trees with $n$ vertices, we obtain an
improved prediction algorithm for graphs with high effective resistance.
In contrast to previous approaches that move the graph problem into problems
in vector space using graph Laplacian and rely on the analysis of the
perceptron algorithm, our proof are purely combinatorial. Further more, our
approach directly generalizes to the case where labels are not binary.
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关键词
graph laplacian,data structure,vector space,discrete mathematics
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