共查询到20条相似文献,搜索用时 15 毫秒
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Raphael Yuster 《Information Processing Letters》2011,111(21-22):1057-1061
We present an algorithm that finds, for each vertex of an undirected graph, a shortest cycle containing it. While for directed graphs this problem reduces to the All-Pairs Shortest Paths problem, this is not known to be the case for undirected graphs.We present a truly sub-cubic randomized algorithm for the undirected case. Given an undirected graph with n vertices and integer weights in , it runs in time where is the exponent of matrix multiplication. As a by-product, our algorithm can be used to determine which vertices lie on cycles of length at most t in time. For the case of bounded real edge weights, a variant of our algorithm solves the problem up to an additive error of ? in time. 相似文献
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We give the first representation-independent hardness results for PAC learning intersections of halfspaces, a central concept class in computational learning theory. Our hardness results are derived from two public-key cryptosystems due to Regev, which are based on the worst-case hardness of well-studied lattice problems. Specifically, we prove that a polynomial-time algorithm for PAC learning intersections of halfspaces (for a constant ) in n dimensions would yield a polynomial-time solution to - (unique shortest vector problem). We also prove that PAC learning intersections of low-weight halfspaces would yield a polynomial-time quantum solution to - and - (shortest vector problem and shortest independent vector problem, respectively). Our approach also yields the first representation-independent hardness results for learning polynomial-size depth-2 neural networks and polynomial-size depth-3 arithmetic circuits. 相似文献
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Michael Thomas 《Information Processing Letters》2012,112(10):386-391
For decision problems defined over Boolean circuits using gates from a restricted set B only, we have for all finite sets B and of gates such that all gates from B can be computed by circuits over gates from . In this note, we show that a weaker version of this statement holds for decision problems defined over Boolean formulae, namely that and for all finite sets B and of Boolean functions such that all can be defined in . 相似文献
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《Journal of Computer and System Sciences》2016,82(5):793-801
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