Many computer vision algorithms include a robust estimation step where model parameters are computed from a data set containing a significant proportion of outliers. The RANSAC algorithm is possibly the most widely us...
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Many computer vision algorithms include a robust estimation step where model parameters are computed from a data set containing a significant proportion of outliers. The RANSAC algorithm is possibly the most widely used robust estimator in the field of computer vision. In the paper we show that under a broad range of conditions, RANSAC efficiency is significantly improved if its hypothesis evaluation step is randomized. A new randomized (hypothesis evaluation) version of the RANSAC algorithm, R-RANSAC, is introduced. Computational savings are achieved by typically evaluating only a fraction of data points for models contaminated with outliers. The idea is implemented in a two-step evaluation procedure. A mathematically tractable class of statistical preverification test of samples is introduced. For this class of preverification test we derive an approximate relation for the optimal setting of its single parameter. The proposed pre-test is evaluated on both synthetic data and real-world problems and a significant increase in speed is shown. (C) 2004 Elsevier B.V. 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 propose a randomized divide-and-conquer technique that leads to improved randomized and deterministic algorithms for NP-hard PATH, MATCHING, and PACKING problems. For the parameterized max-path problem, our randomi...
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We propose a randomized divide-and-conquer technique that leads to improved randomized and deterministic algorithms for NP-hard PATH, MATCHING, and PACKING problems. For the parameterized max-path problem, our randomized algorithm runs in time O(4(k)k(2.7)m) and polynomial space (where m is the number of edges in the input graph), improving the previous best randomized algorithm for the problem that runs in time O(5.44(k)km) and exponential space. Our randomized algorithms for the parameterized MAX r-d MATCHING and MAX r-set PACKING problems run in time 4((r-1)k)n(O(1)) and polynomial space, improving the previous best algorithms for the problems that run in time 10.88(rk)n(O(1)) and exponential space. Moreover, our randomized algorithms can be derandomized to result in significantly improved deterministic algorithms for the problems, and they can be extended to solve other matching and packing problems.
The mesh of buses (MBUS) is a parallel computation model which consists of n x n processors, II row buses and n column buses but no local connections between two neighboring processors. As for deterministic (permutati...
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The mesh of buses (MBUS) is a parallel computation model which consists of n x n processors, II row buses and n column buses but no local connections between two neighboring processors. As for deterministic (permutation) routing on MBUSs, the known 1.5n upper bound appears to be hard to improve. Also, the information theoretic lower bound for any type of MBUS routing is 1.0n. In this paper, we present two randomized algorithms for MBUS routing. One of them runs in 1.4375n + o(n) steps with high probability. The other runs 1.25n + o(n) steps also with high probability but needs more local computation. (C) 2001 Elsevier Science B.V. All rights reserved.
In this paper, we consider a popular randomized broadcasting algorithm called push-algorithm defined as follows. Initially, one vertex of a graph G = (V, E) owns a piece of information which is spread iteratively to a...
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In this paper, we consider a popular randomized broadcasting algorithm called push-algorithm defined as follows. Initially, one vertex of a graph G = (V, E) owns a piece of information which is spread iteratively to all other vertices: in each timestep t = 1, 2, ... every informed vertex chooses a neighbor uniformly at random and informs it. The question is how many time steps are required until all vertices become informed (with high probability). For various graph classes, involved methods have been developed in order to show an upper bound of O(log N + diam(G)) on the runtime of the push-algorithm, where N is the number of vertices and diam(G) denotes the diameter of G. However, no asymptotically tight bound on the runtime based on the mixing time of random walks has been established. In this work we fill this gap by deriving an upper bound of O(T-mix+ logN), where T-mix denotes the mixing time of a certain random walk on G. After that we prove upper bounds that are based on certain edge expansion properties of G. However, for hypercubes neither the bound based on the mixing time nor the bounds based on edge expansion properties are tight. That is why we develop a general way to combine these two approaches by which we can deduce that the runtime of the push-algorithm is Theta (logN) on every Hamming graph.
This paper investigates the convergence of the randomized Kaczmarz algorithm for the problem of phase retrieval of complex-valued objects. Although this algorithm has been studied for the real-valued case in [28], its...
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This paper investigates the convergence of the randomized Kaczmarz algorithm for the problem of phase retrieval of complex-valued objects. Although this algorithm has been studied for the real-valued case in [28], its generalization to the complex-valued case is nontrivial and has been left as a conjecture. This paper applies a different approach by establishing the connection between the convergence of the algorithm and the convexity of an objective function. Based on the connection, it demonstrates that when the sensing vectors are sampled uniformly from a unit sphere in C-n and the number of sensing vectors m satisfies m > O(n log n) as n, m -> infinity, then this algorithm with a good initialization achieves linear convergence to the solution with high probability. The method can be applied to other statistical models of sensing vectors as well. A similar convergence result is established for the unitary model, where the sensing vectors are from the columns of random orthogonal matrices.
Multiple-message broadcast, or k-broadcast, is one of the fundamental problems in network communication. In short, there are k packets distributed across the network, each of them has to be delivered to all other node...
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ISBN:
(纸本)9781450307192
Multiple-message broadcast, or k-broadcast, is one of the fundamental problems in network communication. In short, there are k packets distributed across the network, each of them has to be delivered to all other nodes. We consider this task in the model of multi-hop radio network, in which n nodes interact by transmitting and receiving messages. A message transmitted at a round reaches all neighbors of the transmitter at the end of the same round, but may not be successfully received by some, or even all, of these neighbors. More specifically, a node receives a message at a round if this is the only message that has reached this node in this round. Due to this specific interference-prone nature of radio networks, many communication tasks become more challenging and more costly than in other types of networks, especially in ad-hoc setting in which each node knows only its own id and linear estimates on the basic network parameters, such as the number of nodes n, diameter D and maximum node degree Delta. We design a new randomized k-broadcast algorithm combining the best of two worlds: efficient randomized transmission schedules and network coding. We show that our algorithm accomplishes multi-broadcast in O(log Delta) amortized number of communication rounds per packet, with high probability. This improves over the best previous solution of Bar-Yehuda. Israeli and Itai [5], which guarantees only O(log Delta log n) of amortized number of rounds per packet, with high probability.
Many problems from industrial applications and AI can be encoded as Maximum Satisfiability (MaxSAT). Often, it is more desirable to produce practicable results in very short time compared to optimal solutions after an...
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ISBN:
(纸本)9783030582845;9783030582852
Many problems from industrial applications and AI can be encoded as Maximum Satisfiability (MaxSAT). Often, it is more desirable to produce practicable results in very short time compared to optimal solutions after an arbitrary long computation time. In this paper, we propose Stable Resolving (SR), a novel randomized local search heuristic for MaxSAT with that aim. SR works for both weighted and unweighted instances. Starting from a feasible initial solution, the algorithm repeatedly performs the three steps of perturbation, improvements and solution checking. In the perturbation, the search space is explored at the cost of possibly worsening the current solution. The local improvements work by repeatedly flipping signs of variables in over-satisfied clauses. Finally, the algorithm performs a solution checking in a simulated annealing fashion. We compare our approach to state-of-the-art MaxSAT solvers and show by numerical experiments on benchmark instances from the annual MaxSAT competition that SR performs comparable on average and is even the best solver for particular problem instances.
While random polygon generation from a set of planar points has been widely investigated in the literature, very few works address the construction of a simple polygon with minimum area (MINAP) or maximum area (MAXAP)...
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