文章基本信息

标题：Unique End of Potential Line
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作者：John Fearnley ; Spencer Gordon ; Ruta Mehta 等
期刊名称：LIPIcs : Leibniz International Proceedings in Informatics
电子版ISSN：1868-8969
出版年度：2019
卷号：132
页码：1-15
DOI：10.4230/LIPIcs.ICALP.2019.56
出版社：Schloss Dagstuhl -- Leibniz-Zentrum fuer Informatik
摘要：The complexity class CLS was proposed by Daskalakis and Papadimitriou in 2011 to understand the complexity of important NP search problems that admit both path following and potential optimizing algorithms. Here we identify a subclass of CLS - called UniqueEOPL - that applies a more specific combinatorial principle that guarantees unique solutions. We show that UniqueEOPL contains several important problems such as the P-matrix Linear Complementarity Problem, finding Fixed Point of Contraction Maps, and solving Unique Sink Orientations (USOs). UniqueEOPL seems to a proper subclass of CLS and looks more likely to be the right class for the problems of interest. We identify a problem - closely related to solving contraction maps and USOs - that is complete for UniqueEOPL. Our results also give the fastest randomised algorithm for P-matrix LCP.
关键词：P-matrix linear complementarity problem; unique sink orientation; contraction map; TFNP; total search problems; continuous local search