English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Zendy Plus

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Zendy Tools

Zendy Open

Motivated by online advertisement and exchange settings, greedy randomizedalgorithms for the maximum matching problem have been studied, in which thealgorithm makes (random) decisions that are essentially oblivious to the inputgraph. Any greedy algorithm can achieve performance ratio 0.5, which is theexpected number of matched nodes to the number of nodes in a maximum matching.  Since Aronson, Dyer, Frieze and Suen proved that the Modified RandomizedGreedy (MRG) algorithm achieves performance ratio 0.5 + \epsilon (where\epsilon = frac{1}{4}) on arbitrary graphs in the mid-nineties, no furtherattempts in the literature have been made to improve this theoretical ratio forarbitrary graphs until two papers were published in FOCS 2012. Poloczek andSzegedy also analyzed the MRG algorithm to give ratio 0.5039, while Goel andTripathi used experimental techniques to analyze the Ranking algorithm to giveratio 0.56. However, we could not reproduce the experimental results of Goeland Tripathi.  In this paper, we revisit the Ranking algorithm using the LP framework.Special care is given to analyze the structural properties of the Rankingalgorithm in order to derive the LP constraints, of which one known as the\emph{boundary} constraint requires totally new analysis and is crucial to thesuccess of our LP.  We use continuous LP relaxation to analyze the limiting behavior as thefinite LP grows. Of particular interest are new duality and complementaryslackness characterizations that can handle the monotone and the boundaryconstraints in continuous LP. We believe our work achieves the currently besttheoretical performance ratio of \frac{2(5-\sqrt{7})}{9} \approx 0.523 onarbitrary graphs. Moreover, experiments suggest that Ranking cannot performbetter than 0.724 in general.

Ranking on Arbitrary Graphs: Rematch via Continuous LP with Monotone and Boundary Condition Constraints