In this paper we propose a randomized algorithm which can solve the satisfiability problem with the probability of failure not exceeding epsilon in polynomial average time.
In this paper we propose a randomized algorithm which can solve the satisfiability problem with the probability of failure not exceeding epsilon in polynomial average time.
Given an array of n input numbers, the range-maxima problem is that of preprocessing the data so that queries of the type "what is the maximum value in subarray [i..j]" can be answered quickly using one proc...
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The chromatic number of a graph is the minimum number of colors needed to color the vertices such that adjacent vertices receive different colors. The chromatic index is the minimum number of colors needed to color t...
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The chromatic number of a graph is the minimum number of colors needed to color the vertices such that adjacent vertices receive different colors. The chromatic index is the minimum number of colors needed to color the edges such that adjacent edges receive different colors. An analysis presents tight upper and lower bounds for on-line edge coloring and proves that the greedy strategy is optimal. The proofs hold only for graphs for which the maximal degree is relatively small, at most log n. An on-line algorithm has to make decisions after having seen only a subset of the input. For coloring problems, there are 2 natural on-line models - the input is given either vertex-by-vertex or edge-by-edge. The algorithm assigns a color to the current vertex or edge based only on past history. Color assignments cannot be changed. An interesting open problem is whether better bounds can be achieved for graphs whose maximal degree is larger.
We use here the results on the influence graph(1) to adapt them for particular cases where additional information is available. In some cases, it is possible to improve the expected randomized complexity of algorithms...
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We use here the results on the influence graph(1) to adapt them for particular cases where additional information is available. In some cases, it is possible to improve the expected randomized complexity of algorithms from O(n log n) to O(n log(star) n). This technique applies in the following applications: triangulation of a simple polygon, skeleton of a simple polygon, Delaunay triangulation of points knowing the EMST (euclidean minimum spanning tree).
The Delaunay Tree is a hierarchical data structure that has been introduced in [6] and analyzed in [7, 4]. For a given set of sites L in the plane and an order of insertion for these sites, the Delaunay Tree stores al...
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The design and analysis of adaptive sorting algorithms has made important contributions to both theory and practice. The main contributions from the theoretical point of view are: the description of the complexity of ...
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The design and analysis of adaptive sorting algorithms has made important contributions to both theory and practice. The main contributions from the theoretical point of view are: the description of the complexity of a sorting algorithm not only in terms of the size of a problem instance but also in terms of the disorder of the given problem instance;the establishment of new relationships among measures of disorder;the introduction of new sorting algorithms that take advantage of the existing order in the input sequence;and, the proofs that several of the new sorting algorithms achieve maximal (optimal) adaptivity with respect to several measures of disorder. The main contributions from the practical point of view are: the demonstration that several algorithms currently in use are adaptive;and, the development of new algorithms, similar to currently used algorithms that perform competitively on random sequences and are significantly faster on nearly sorted sequences. In this survey, we present the basic notions and concepts of adaptive sorting and the state of the art of adaptive sorting algorithms.
We present two randomized algorithms. One solves linear programs involving m constraints in d variables in expected time O(m). The other constructs convex hulls of n points in R(d), d > 3, in expected time O(n[d/2]...
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We present two randomized algorithms. One solves linear programs involving m constraints in d variables in expected time O(m). The other constructs convex hulls of n points in R(d), d > 3, in expected time O(n[d/2]). In both bounds d is considered to be a constant. In the linear programming algorithm the dependence of the time bound on d is of the form d!. The main virtue of our results lies in the utter simplicity of the algorithms as well as their analyses.
This paper gives efficient, randomized algorithms for the following problems: (1) construction of levels of order 1 to k in an arrangement of hyperplanes in any dimension and (2) construction of higher-order Voronoi d...
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This paper gives efficient, randomized algorithms for the following problems: (1) construction of levels of order 1 to k in an arrangement of hyperplanes in any dimension and (2) construction of higher-order Voronoi diagrams of order 1 to k in any dimension. A new combinatorial tool in the form of a mathematical series, called a theta series, is associated with an arrangement of hyperplanes in R(d). It is used to study the combinatorial as well as algorithmic complexity of the geometric problems under consideration.
All known fast randomized Byzantine Agreement (BA) protocols have (rare) infinite runs. We present a method of combining a randomized BA protocol of a certain class with any deterministic BA protocol to obtain a rando...
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All known fast randomized Byzantine Agreement (BA) protocols have (rare) infinite runs. We present a method of combining a randomized BA protocol of a certain class with any deterministic BA protocol to obtain a randomized protocol that preserves the expected average complexity of the randomized protocol while guaranteeing termination in all runs. In particular, we obtain a randomized BA protocol with constant expected time, which always terminates within t + O(log t) rounds, where t = O(n) is the number of faulty processors.
Three parameters characterize the performance of a probabilistic algorithm: T, the run-time of the algorithm; Q, the probability that the algorithm fails to complete the computation in the first T steps; and R, the am...
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Three parameters characterize the performance of a probabilistic algorithm: T, the run-time of the algorithm; Q, the probability that the algorithm fails to complete the computation in the first T steps; and R, the amount of randomness used by the algorithm, measured by the entropy of its random source. A tight trade-off between these three parameters for the problem of oblivious packet routing on N-vertex bounded-degree networks is presented. A (
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