منابع مشابه
Finding Even Subgraphs Even Faster
Problems of the following kind have been the focus of much recent research in the realm of parameterized complexity: Given an input graph (digraph) on n vertices and a positive integer parameter k, find if there exist k edges (arcs) whose deletion results in a graph that satisfies some specified parity constraints. In particular, when the objective is to obtain a connected graph in which all th...
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We describe efficient algorithms for finding even cycles in undirected graphs. Our main results are the following: (i) For every k ≥ 2, there is an O(V ) time algorithm that decides whether an undirected graph G = (V,E) contains a simple cycle of length 2k and finds one if it does. (ii) There is an O(V ) time algorithm that finds a shortest even cycle in an undirected graph G = (V,E).
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We give a new proof of Fürer's bound for the cost of multiplying n-bit integers in the bit complexity model. Unlike Fürer, our method does not require constructing special coecient rings with fast roots of unity. Moreover, we prove the more explicit bound O(n logn K log n) with K = 8. We show that an optimised variant of Fürer's algorithm achieves only K = 16, suggesting that the new algorithm ...
متن کاملMaking k-means Even Faster
The k-means algorithm is widely used for clustering, compressing, and summarizing vector data. In this paper, we propose a new acceleration for exact k-means that gives the same answer, but is much faster in practice. Like Elkan’s accelerated algorithm [8], our algorithm avoids distance computations using distance bounds and the triangle inequality. Our algorithm uses one novel lower bound for ...
متن کاملOn Even-Degree Subgraphs of Linear Hypergraphs
A subgraph of a hypergraph H is even if all its degrees are positive even integers, and b-bounded if it has maximum degree at most b. Let fb(n) denote the maximum number of edges in a linear nvertex 3-uniform hypergraph which does not contain a b-bounded even subgraph. In this paper, we show that if b ≥ 12, then n logn 3b log logn ≤ fb(n) ≤ Bn(logn) for some absolute constant B, thus establishi...
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ژورنال
عنوان ژورنال: Journal of Computer and System Sciences
سال: 2018
ISSN: 0022-0000
DOI: 10.1016/j.jcss.2018.03.001