In this paper we propose and analyze a randomized algorithm to get rendezvous between neighbours in an anonymous graph. We examine in particular the probability to obtain at least one rendezvous and the expected numbe...
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In this paper we propose and analyze a randomized algorithm to get rendezvous between neighbours in an anonymous graph. We examine in particular the probability to obtain at least one rendezvous and the expected number of rendezvous. We study the rendezvous number distribution in the cases of chain graphs, rings, and complete graphs. The last part is devoted to the efficiency of the proposed algorithm. (C) 2003 Elsevier Science (USA). All rights reserved.
We design and analyze a randomized one-passage election algorithm in trees based on a result of Angluin in [Proceedings of the 12th Symposium on Theory of Computing, 1980, pp. 82]. The election process is a distribute...
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We design and analyze a randomized one-passage election algorithm in trees based on a result of Angluin in [Proceedings of the 12th Symposium on Theory of Computing, 1980, pp. 82]. The election process is a distributed elimination scheme which removes leaves one-by-one reducing the tree to a single vertex, called the leader (or elected vertex). We define a locally computable parameter guiding randomly the elimination process. As a particular instance, we provide a parameter assignment in a Markovian type random process in which all vertices have the same chance of being elected. (c) 2005 Elsevier Inc. All rights reserved.
We present a new randomized algorithm for checking the satisfiability of a conjunction of literals in the combined theory of linear equalities and uninterpreted functions. The key idea of the algorithm is to process t...
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We present a new randomized algorithm for checking the satisfiability of a conjunction of literals in the combined theory of linear equalities and uninterpreted functions. The key idea of the algorithm is to process the literals incrementally and to maintain at all times a set of random variable assignments that satisfy the literals seen so far. We prove that this algorithm is complete (i.e., it identifies all unsatisfiable conjunctions) and is probabilistically sound (i.e., the probability that it fails to identify satisfiable conjunctions is very small). The algorithm has the ability to retract assumptions incrementally with almost no additional space overhead. The algorithm can also be easily adapted to produce proofs for its output. The key advantage of the algorithm is its simplicity. We also show experimentally that the randomized algorithm has performance competitive with the existing deterministic symbolic algorithms. (c) 2005 Elsevier Inc. All rights reserved.
In this paper we consider an on-line scheduling problem, where jobs with similar processing times within [1, r] arrive one by one to be scheduled in an on-line setting on two identical parallel processors without pree...
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In this paper we consider an on-line scheduling problem, where jobs with similar processing times within [1, r] arrive one by one to be scheduled in an on-line setting on two identical parallel processors without preemption. The objective is to nlinimize makespan. We devise a randomized on-line algorithm for this problem along with a lower bound.
We present a new randomized algorithm for checking the satisfiability of a conjunction of literals in the combined theory of linear equalities and uninterpreted functions. The key idea of the algorithm is to process t...
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ISBN:
(纸本)3540405593
We present a new randomized algorithm for checking the satisfiability of a conjunction of literals in the combined theory of linear equalities and uninterpreted functions. The key idea of the algorithm is to process the literals incrementally and to maintain at all times a set of random variable assignments that satisfy the literals seen so far. We prove that this algorithm is complete (i.e., it identifies all unsatisfiable conjunctions) and is probabilistically sound (i.e., the probability that it fails to identify satisfiable conjunctions is very small). The algorithm has the ability to retract assumptions incrementally with almost no additional space overhead. The algorithm can also be easily adapted to produce proofs for its output. The key advantage of the algorithm is its simplicity. We also show experimentally that the randomized algorithm has performance competitive with the existing deterministic symbolic algorithms. (c) 2005 Elsevier Inc. All rights reserved.
We propose an efficient and accurate randomized approximation algorithm for computing the price of European-Asian options. Our algorithm can be seen as a modification of the approximation algorithm developed by Aingwo...
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We propose an efficient and accurate randomized approximation algorithm for computing the price of European-Asian options. Our algorithm can be seen as a modification of the approximation algorithm developed by Aingworth et al. (2000) into a randomized algorithm, which improves the accuracy theoretically as well as practically. We also propose a new option named the Saving-Asian option which enjoys advantages of both the European-Asian and American-Asian options. It is shown that our approximation algorithm also works for pricing Saving-Asian options.
Probabilistic roadmap (PRM) planners have been successful in path planning of robots with many degrees of freedom, but sampling narrow passages in a robot's configuration space remains a challenge for PRM planners...
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Probabilistic roadmap (PRM) planners have been successful in path planning of robots with many degrees of freedom, but sampling narrow passages in a robot's configuration space remains a challenge for PRM planners. This paper presents a hybrid sampling strategy in the PRM framework for finding paths through narrow passages. A key ingredient of the new strategy is the bridge test, which reduces sample density in many unimportant parts of a configuration space, resulting in increased sample density in narrow passages. The bridge test can be implemented efficiently in high-dimensional configuration spaces using only simple tests of local geometry. The strengths of the bridge test and uniform sampling complement each other naturally. The two sampling strategies are combined to construct the hybrid sampling strategy for our planner. We implemented the planner and tested it on rigid and articulated robots in 2-D and 3-D environments. Experiments show that the hybrid sampling strategy enables relatively small roadmaps to reliably capture the connectivity of configuration spaces with difficult narrow passages.
Distributed hash table (DHT) systems are an important class of peer-to-peer routing infrastructures. They enable scalable wide-area storage and retrieval of information, and will support the rapid development of a wid...
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Distributed hash table (DHT) systems are an important class of peer-to-peer routing infrastructures. They enable scalable wide-area storage and retrieval of information, and will support the rapid development of a wide variety of Internet-scale applications ranging from naming systems and file systems to application-layer multicast. DHT systems essentially build an overlay network, but a path on the overlay between any two nodes can be significantly different from the unicast path between those two nodes on the underlying network. As such, the lookup latency in these systems can be quite high and can adversely impact the performance of applications built on top of such systems. In this paper, we discuss a random sampling technique that incrementally improves lookup latency in DHT systems. Our sampling can be implemented using information gleaned from lookups traversing the overlay network. For this reason, we call our approach lookup-parasitic random sampling (LPRS). LPRS converges quickly, and requires relatively few modifications to existing DHT systems. For idealized versions of DHT systems like Chord, Tapestry, and Pastry, we analytically prove that LPRS can result in lookup latencies proportional to the average unicast latency of the network, provided the underlying physical topology has a power-law latency expansion. We then validate this analysis by implementing LPRS in the Chord simulator. Our simulations reveal that LPRS-Chord exhibits a qualitatively better latency scaling behavior relative to unmodified Chord. The overhead of LPRS is one sample per lookup hop in the worst case. Finally, we provide evidence which suggests that the Internet router-level topology resembles power-law latency expansion. This finding implies that LPRS has significant practical applicability as a general latency reduction technique for many DHT systems, This finding is also of independent interest since it might inform the design of latency-sensitive topology models for the Inte
Given a bipartite graph G = (V, W, E), a 2-layered drawing consists of placing nodes in the first node set V on a straight line L-1 and placing nodes in the second node set Won a parallel line L-2. For a given orderin...
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Given a bipartite graph G = (V, W, E), a 2-layered drawing consists of placing nodes in the first node set V on a straight line L-1 and placing nodes in the second node set Won a parallel line L-2. For a given ordering of nodes in Won L2, the one-sided crossing minimization problem asks to find an ordering of nodes in V on L-1 so that the number of arc crossings is minimized. A well-known lower bound LB on the minimum number of crossings is obtained by summing up min{c(uv), c(vu)} over all node pairs u, v is an element of V, where c(uv) denotes the number of crossings generated by arcs incident to u and v when u precedes v in an ordering. In this paper, we prove that there always exists a solution whose crossing number is at most (1.2964 + 12/(delta - 4))LB if the minimum degree delta of a node in V is at least 5. (c) 2004 Elsevier B.V. All rights reserved.
We present new baby steps/giant steps algorithms of asymptotically fast running time for dense matrix problems. Our algorithms compute the determinant, characteristic polynomial, Frobenius normal form and Smith normal...
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We present new baby steps/giant steps algorithms of asymptotically fast running time for dense matrix problems. Our algorithms compute the determinant, characteristic polynomial, Frobenius normal form and Smith normal form of a dense n x n matrix A with integer entries in ( n(3.2) log \\A\\s)(1+o( 1)) and ( n(2.697263) log \\A\\) (1+o( 1)) bit operations;here \\A\\ denotes the largest entry in absolute value and the exponent adjustment by "+o(1)" captures additional factors C-1( log n) (C2)( loglog \\A\\)(C3) for positive real constants C1, C2, C3. The bit complexity ( n(3.2) log \\A\\)(1+o( 1)) results from using the classical cubic matrix multiplication algorithm. Our algorithms are randomized, and we can certify that the output is the determinant of A in a Las Vegas fashion. The second category of problems deals with the setting where the matrix A has elements from an abstract commutative ring, that is, when no divisions in the domain of entries are possible. We present algorithms that deterministically compute the determinant, characteristic polynomial and adjoint of A with n(3.2+o( 1)) and O(n(2.697263)) ring additions, subtractions and multiplications.
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