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Output-sensitive algorithm

About: Output-sensitive algorithm is a(n) research topic. Over the lifetime, 751 publication(s) have been published within this topic receiving 30567 citation(s). more


Journal ArticleDOI: 10.1109/18.910572
Abstract: Algorithms that must deal with complicated global functions of many variables often exploit the manner in which the given functions factor as a product of "local" functions, each of which depends on a subset of the variables. Such a factorization can be visualized with a bipartite graph that we call a factor graph, In this tutorial paper, we present a generic message-passing algorithm, the sum-product algorithm, that operates in a factor graph. Following a single, simple computational rule, the sum-product algorithm computes-either exactly or approximately-various marginal functions derived from the global function. A wide variety of algorithms developed in artificial intelligence, signal processing, and digital communications can be derived as specific instances of the sum-product algorithm, including the forward/backward algorithm, the Viterbi algorithm, the iterative "turbo" decoding algorithm, Pearl's (1988) belief propagation algorithm for Bayesian networks, the Kalman filter, and certain fast Fourier transform (FFT) algorithms. more

Topics: Factor graph (72%), Forward algorithm (66%), Belief propagation (66%) more

6,196 Citations

Open accessJournal ArticleDOI: 10.1145/235815.235821
Abstract: The convex hull of a set of points is the smallest convex set that contains the points. This article presents a practical convex hull algorithm that combines the two-dimensional Quickhull algorithm with the general-dimension Beneath-Beyond Algorithm. It is similar to the randomized, incremental algorithms for convex hull and delaunay triangulation. We provide empirical evidence that the algorithm runs faster when the input contains nonextreme points and that it used less memory. computational geometry algorithms have traditionally assumed that input sets are well behaved. When an algorithm is implemented with floating-point arithmetic, this assumption can lead to serous errors. We briefly describe a solution to this problem when computing the convex hull in two, three, or four dimensions. The output is a set of “thick” facets that contain all possible exact convex hulls of the input. A variation is effective in five or more dimensions. more

Topics: Convex hull algorithms (76%), Convex hull (75%), Convex set (73%) more

4,540 Citations

Proceedings ArticleDOI: 10.1145/73393.73394
Kenneth L. Clarkson1Institutions (1)
06 Jan 1988-
Abstract: Random sampling is used for several new geometric algorithms. The algorithms are “Las Vegas,” and their expected bounds are with respect to the random behavior of the algorithms. One algorithm reports all the intersecting pairs of a set of line segments in the plane, and requires O(A + n log n) expected time, where A is the size of the answer, the number of intersecting pairs reported. The algorithm requires O(n) space in the worst case. Another algorithm computes the convex hull of a point set in E3 in O(n log A) expected time, where n is the number of points and A is the number of points on the surface of the hull. A simple Las Vegas algorithm triangulates simple polygons in O(n log log n) expected time. Algorithms for half-space range reporting are also given. In addition, this paper gives asymptotically tight bounds for a combinatorial quantity of interest in discrete and computational geometry, related to halfspace partitions of point sets. more

Topics: Las Vegas algorithm (64%), Output-sensitive algorithm (63%), Randomized algorithm (61%) more

1,138 Citations

Open accessPosted Content
Abstract: We introduce a quantum algorithm that produces approximate solutions for combinatorial optimization problems. The algorithm depends on a positive integer p and the quality of the approximation improves as p is increased. The quantum circuit that implements the algorithm consists of unitary gates whose locality is at most the locality of the objective function whose optimum is sought. The depth of the circuit grows linearly with p times (at worst) the number of constraints. If p is fixed, that is, independent of the input size, the algorithm makes use of efficient classical preprocessing. If p grows with the input size a different strategy is proposed. We study the algorithm as applied to MaxCut on regular graphs and analyze its performance on 2-regular and 3-regular graphs for fixed p. For p = 1, on 3-regular graphs the quantum algorithm always finds a cut that is at least 0.6924 times the size of the optimal cut. more

1,088 Citations

Open accessJournal ArticleDOI: 10.1007/BF01580113
Jack Edmonds1, Ellis L. Johnson2Institutions (2)
Abstract: The solution of the Chinese postman problem using matching theory is given. The convex hull of integer solutions is described as a linear programming polyhedron. This polyhedron is used to show that a good algorithm gives an optimum solution. The algorithm is a specialization of the more generalb-matching blossom algorithm. Algorithms for finding Euler tours and related problems are also discussed. more

Topics: Route inspection problem (58%), Convex polytope (57%), Output-sensitive algorithm (57%) more

908 Citations

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Topic's top 5 most impactful authors

Bernard Chazelle

7 papers, 1.1K citations

Godfried T. Toussaint

7 papers, 196 citations

Witold Pedrycz

4 papers, 35 citations

Mohammadreza Razzazi

4 papers, 1 citations

Timothy M. Chan

4 papers, 105 citations

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