A method of approximate filtration of noise reflections is proposed for measurement of the coordinates of an object with a sound emitter moving in an aquatic environment. A passive hydroacoustic detection and ranging ...
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A method of approximate filtration of noise reflections is proposed for measurement of the coordinates of an object with a sound emitter moving in an aquatic environment. A passive hydroacoustic detection and ranging system based on a network of hydrophones is used in the measurements. A two-stage approximation algorithm is employed for digital processing of the Doppler hydroacoustic signals from the outputs of the hydrophones. An example illustrating implementation of the filtration method and its error is considered.
Wireless Sensor Networks (WSNs) are gaining more interest in a variety of applications. Of their different characteristics and challenges, network management and lifetime elongation are the most considered issues in W...
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Wireless Sensor Networks (WSNs) are gaining more interest in a variety of applications. Of their different characteristics and challenges, network management and lifetime elongation are the most considered issues in WSN based systems. Connected Dominating Set (CDS) is known to be an efficient strategy to control network topology, reduce overhead, and extend network lifetime. Designing a CDS algorithm for WSNs is very challenging. This paper provides a review on connected dominating set construction techniques for wireless sensor networks.
We give the first efficient (1-epsilon)-approximation algorithm for the following problem: Given an axis-parallel d-dimensional box R in a"e (d) containing n points, compute a maximum-volume empty axis-parallel d...
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We give the first efficient (1-epsilon)-approximation algorithm for the following problem: Given an axis-parallel d-dimensional box R in a"e (d) containing n points, compute a maximum-volume empty axis-parallel d-dimensional box contained in R. The minimum of this quantity over all such point sets is of the order . Our algorithm finds an empty axis-aligned box whose volume is at least (1-epsilon) of the maximum in O((8ed epsilon (-2)) (d) a <...nlog (d) n) time. No previous efficient exact or approximation algorithms were known for this problem for da parts per thousand yen4. As the problem has been recently shown to be NP-hard in arbitrarily high dimensions (i.e., when d is part of the input), the existence of an efficient exact algorithm is unlikely. We also present a (1-epsilon)-approximation algorithm that, given an axis-parallel d-dimensional cube R in a"e (d) containing n points, computes a maximum-volume empty axis-parallel hypercube contained in R. The minimum of this quantity over all such point sets is also shown to be of the order . A faster (1-epsilon)-approximation algorithm, with a milder dependence on d in the running time, is obtained in this case.
Rooted triplets are becoming one of the most important types of input for reconstructing rooted phylogenies. A rooted triplet is a phylogenetic tree on three leaves and shows the evolutionary relationship of the corre...
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Rooted triplets are becoming one of the most important types of input for reconstructing rooted phylogenies. A rooted triplet is a phylogenetic tree on three leaves and shows the evolutionary relationship of the corresponding three species. In this paper, we investigate the problem of inferring the maximum consensus evolutionary tree from a set of rooted triplets. This problem is known to be APX-hard. We present two new heuristic algorithms. For a given set of m triplets on n species, the FastTree algorithm runs in O (m + alpha (n)n(2)) time, where alpha (n) is the functional inverse of Ackermann's function. This is faster than any other previously known algorithms, although the outcome is less satisfactory. The Best Pair Merge with Total Reconstruction (BPMTR) algorithm runs in O (mn(3)) time and, on average, performs better than any other previously known algorithms for this problem.
A subset F of vertices of a graph G is called a vertex cover P-k set if every path of order k in G contains at least one vertex from F. Denote by psi(k)(G) the minimum cardinality of a vertex cover P-k set in G. The v...
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A subset F of vertices of a graph G is called a vertex cover P-k set if every path of order k in G contains at least one vertex from F. Denote by psi(k)(G) the minimum cardinality of a vertex cover P-k set in G. The vertex cover P-k (VCPk) problem is to find a minimum vertex cover P-k set. In this paper, we restrict our attention to the VCP3 problem in cubic graphs. This paper proves that the VCP3 problem is NP-hard for cubic planar graphs of girth 3. Further we give sharp lower and upper bounds on psi(3)(G) for cubic graphs and propose a 1.57-approximation algorithm for the VCP3 problem in cubic graphs. (C) 2013 Elsevier B.V. All rights reserved.
In this letter we investigate link scheduling algorithms for throughput maximization in multicast wireless networks. According to our system model, each source node transmits to a multicast group that resides one hop ...
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In this letter we investigate link scheduling algorithms for throughput maximization in multicast wireless networks. According to our system model, each source node transmits to a multicast group that resides one hop away. We adopt the physical interference model to reflect the aggregate signal to interference and noise ratio (SINR) at each node of the multicast group. We present an ILP formulation of the aforementioned problem. The basic feature of the problem formulation is that it decomposes the single multicast session into the corresponding point-to-point links. The rationale is that a solution algorithm has more flexibility regarding the scheduling options for individual nodes. The extended MILP problem that also considers power control is solved with LP relaxation. Performance results for both the ILP and MILP problems are obtained for different traffic loads and different number of nodes per multicast group.
The hard-core model has received much attention in the past couple of decades as a lattice gas model with hard constraints in statistical physics, a multicast model of calls in communication networks, and as a weighte...
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The hard-core model has received much attention in the past couple of decades as a lattice gas model with hard constraints in statistical physics, a multicast model of calls in communication networks, and as a weighted independent set problem in combinatorics, probability and theoretical computer science. In this model, each independent set I in a graph G is weighted proportionally to lambda(|I|), for a positive real parameter lambda. For large lambda, computing the partition function (namely, the normalizing constant which makes the weighting a probability distribution on a finite graph) on graphs of maximum degree Delta a parts per thousand yen 3, is a well known computationally challenging problem. More concretely, let denote the critical value for the so-called uniqueness threshold of the hard-core model on the infinite Delta-regular tree;recent breakthrough results of Weitz (Proceedings of the 38th Annual ACM Symposium on Theory of Computing (STOC), pp. 140-149, 2006) and Sly (Proceedings of the 51st Annual IEEE Symposium on Foundations of Computer Science (FOCS), pp. 287-296, 2010) have identified as a threshold where the hardness of estimating the above partition function undergoes a computational transition. We focus on the well-studied particular case of the square lattice , and provide a new lower bound for the uniqueness threshold, in particular taking it well above . Our technique refines and builds on the tree of self-avoiding walks approach of Weitz, resulting in a new technical sufficient criterion (of wider applicability) for establishing strong spatial mixing (and hence uniqueness) for the hard-core model. Our new criterion achieves better bounds on strong spatial mixing when the graph has extra structure, improving upon what can be achieved by just using the maximum degree. Applying our technique to we prove that strong spatial mixing holds for all lambda < 2.3882, improving upon the work of Weitz that held for lambda < 27/16 = 1.6875. Our results
We consider the k-Directed Steiner Forest (k-DSF) problem: Given a directed graph G = (V, E) with edge costs, a collection D subset of V x V of ordered node pairs, and an integer k <= vertical bar D vertical bar, f...
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We consider the k-Directed Steiner Forest (k-DSF) problem: Given a directed graph G = (V, E) with edge costs, a collection D subset of V x V of ordered node pairs, and an integer k <= vertical bar D vertical bar, find a minimum cost subgraph H of G that contains an st-path for (at least) k pairs (s, t) is an element of D. When k = vertical bar D vertical bar, we get the Directed Steiner Forest (DSF) problem. The best known approximation ratios for these problems are: (O) over tilde (k(2/3)) for k-DSF by Charikar et al. (1999)[6], and O(k(1/2+epsilon)) for DSF by Chekuri et al. (2008)[7]. Our main result is achieving the first sub-linear in terms of n = vertical bar V vertical bar approximation ratio for DSF. Specifically, we give an O(n(epsilon).min{n(4/5), m(2/3)})-approximation scheme for DSF. For k-DSF we give a simple greedy O(k(1/2+epsilon))-approximation algorithm. This improves upon the best known ratio (O) over tilde (k(2/3)) by Charikar et al. (1999) [6], and (almost) matches, in terms of k, the best ratio known for the undirected variant (Gupta et al., 2010 [18]). This algorithm uses a new structure called start-junction tree which may be of independent interest. (C) 2011 Elsevier Inc. All rights reserved.
In this note,we provide an almost tight lower bound for the scheduling problem to meet two min-sum objectives considered by Angel et *** ***.35(1):69–73,2007.
In this note,we provide an almost tight lower bound for the scheduling problem to meet two min-sum objectives considered by Angel et *** ***.35(1):69–73,2007.
Given a simple polygon Q drawn on a piece of planar material R, we cut Q out of R by a circular saw with a total number of cuts no more than twice the optimal. This improves the previous approximation ratio of 2.5 obt...
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Given a simple polygon Q drawn on a piece of planar material R, we cut Q out of R by a circular saw with a total number of cuts no more than twice the optimal. This improves the previous approximation ratio of 2.5 obtained by Demaine et *** 2001.
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