Formulas are given for the expected number of nodes in the backtrack tree that is generated while searching for all the solutions of a random predicate. The most general formulas apply to selection from any set of pre...
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Formulas are given for the expected number of nodes in the backtrack tree that is generated while searching for all the solutions of a random predicate. The most general formulas apply to selection from any set of predicates that obeys the following conditions. Each predicate is the conjunction of t terms selected from a set of terms T. For any subset T′≦
In this paper, we consider the problem of multicasting a message in k-ary n-cubes under the store-and-forward model. The objective of the problem is to minimize the size of the resultant multicast tree by keeping the ...
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In this paper, we consider the problem of multicasting a message in k-ary n-cubes under the store-and-forward model. The objective of the problem is to minimize the size of the resultant multicast tree by keeping the distance to each destination over the tree the same as the distance in the original graph. In the following, we first propose an algorithm that grows a multicast tree in a greedy manner, in the sense that for each intermediate vertex of the tree, the outgoing edges of the vertex are selected in a non-increasing order of the number of destinations that can use the edge in a shortest path to the destination. We then evaluate the goodness of the algorithm in terms of the worst case ratio of the size of the generated tree to the size of an optimal tree. It is proved that for any k greater than or equal to 5 and n greater than or equal to 6, the performnance ratio of the greedy algorithm is c x kn - o(n) for some constant 1/12 less than or equal to c less than or equal to 1/2.
This paper shows that we could describe the characteristics of easy and hard fitness landscapes in one-dimensional continuous space by drift analysis. The work expends the existing results in the discrete space into t...
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ISBN:
(纸本)0780385152
This paper shows that we could describe the characteristics of easy and hard fitness landscapes in one-dimensional continuous space by drift analysis. The work expends the existing results in the discrete space into the continue space. A fitness landscape, in this paper, is regarded as the behaviour of an evolutionary algorithm on fitness functions. Based on the drift analysis, easy fitness landscapes are thought to be a "short-distance" landscape, which is easy for the evolutionary algorithm to find the optimal point;and hard fitness landscapes then are as a far-distance landscape, which the evolutionary algorithm had to spend a long time to find the optimal point.
Based on earlier work on amortised resource analysis, we establish a novel automated amortised resource analysis for term rewrite systems. The method is presented in an inference system akin to a type system and gives...
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ISBN:
(数字)9783319906867
ISBN:
(纸本)9783319906867;9783319906850
Based on earlier work on amortised resource analysis, we establish a novel automated amortised resource analysis for term rewrite systems. The method is presented in an inference system akin to a type system and gives rise to polynomial bounds on the innermost runtime complexity of the analysed term rewrite system. Our analysis does not restrict the input rewrite system in any way. This facilitates integration in a general framework for resource analysis of programs. In particular, we have implemented the method and integrated it into our tool T subset of T.
In this paper, we consider the problem of multicasting a message in k-ary n-cubes under the store-and-forward model. The objective of the problem is to minimize the size of the resultant multicast tree by keeping the ...
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ISBN:
(纸本)0769516777
In this paper, we consider the problem of multicasting a message in k-ary n-cubes under the store-and-forward model. The objective of the problem is to minimize the size of the resultant multicast tree by keeping the distance to each destination over the tree the same as the distance in the original graph. In the following, we first propose an algorithm that grows a multicast tree in a greedy manner, in the sense that for each intermediate vertex of the tree, the outgoing edges of the vertex are selected in a non-increasing order of the number of destinations that can use the edge in a shortest path to the destination. We then evaluate the goodness of the algorithm in terms of the worst case ratio of the size of the generated tree to the size of an optimal tree. It is proved that for any k greater than or equal to 5 and n greater than or equal to 6, the performance ratio of the greedy algorithm is c x kn - o(n) for some constant 1/12 less than or equal to c less than or equal to 1/2.
We analyze the implementation of set operations using binary tries. Our techniques are substantially simpler than previous techniques used for this problem, and allow us to analysis not only the expected performance b...
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We present some recent results on the probabilistic behaviour of interior point methods for the convex conic feasibility problem and for homotopy methods solving complex polynomial equations. As suggested by Spielman ...
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ISBN:
(纸本)9789814324342
We present some recent results on the probabilistic behaviour of interior point methods for the convex conic feasibility problem and for homotopy methods solving complex polynomial equations. As suggested by Spielman and Teng, the goal is to prove that for all inputs (even ill-posed ones), and all slight random perturbations of that input, it is unlikely that the running time will be large. These results are obtained through a probabilistic analysis of the condition of the corresponding computational problems.
A key problem in computational geometry is the identification of subsets of a point set having particular properties. We study this problem for the properties of convexity and emptiness. We show that finding empty tri...
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A key problem in computational geometry is the identification of subsets of a point set having particular properties. We study this problem for the properties of convexity and emptiness. We show that finding empty triangles is related to the problem of determining pairs of vertices that see each other in a star-shaped polygon. A linear-time algorithm for this problem which is of independent interest yields an optimal algorithm for finding all empty triangles. This result is then extended to an algorithm for finding empty convex r-gons (r> 3) and for determining a largest empty convex subset. Finally, extensions to higher dimensions are mentioned.
We provide sharp estimates for the probabilistic behaviour of the main parameters of the Euclid algorithms, both on polynomials and on integer numbers. We study in particular the distribution of the bit-complexity whi...
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We provide sharp estimates for the probabilistic behaviour of the main parameters of the Euclid algorithms, both on polynomials and on integer numbers. We study in particular the distribution of the bit-complexity which involves two main parameters: digit-costs and length of remainders. We first show here that an asymptotic Gaussian law holds for the length of remainders at a fraction of the execution, which exhibits a deep regularity phenomenon. Then, we study in each framework-polynomials (P) and integer numbers (I)-two gcd algorithms, the standard one (S) which only computes the gcd, and the extended one (E) which also computes the Bezout pair, and is widely used for computing modular inverses. The extended algorithm is more regular than the standard one, and this explains that our results are more precise for the Extended algorithm: we exhibit an asymptotic Gaussian law for the bit-complexity of the extended algorithm, in both cases (P) and (I). We also prove that an asymptotic Gaussian law for the bit-complexity of the standard gcd in case (P), but we do not succeed obtaining a similar result in case (I). The integer study is more involved than the polynomial study, as it is usually the case. In the polynomial case, we deal with the central tools of the distributional analysis of algorithms, namely bivariate generating functions. In the integer case, we are led to dynamical methods, which heavily use the dynamical system underlying the number Euclidean algorithm, and its transfer operator. Baladi and Vallee (J. Number Theory 110(2):331-386, 2005) have recently designed a general framework for "distributional dynamical analysis", where they have exhibited asymptotic Gaussian laws for a large family of parameters. However, this family does not contain neither the bit-complexity cost nor the size of remainders, and we have to extend their methods for obtaining our results. Even if these dynamical methods are not necessary in case (P), we explain how the polynomial
We devise time-space optimal methods for stably performing set and multiset operations on sorted files of data. For the sake of complete generality, our techniques neither modify records nor require any information ot...
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We devise time-space optimal methods for stably performing set and multiset operations on sorted files of data. For the sake of complete generality, our techniques neither modify records nor require any information other than a record's key.
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