We introduce a generalization of interval graphs, which we call Dotted Interval Graphs (DIG). A dotted interval graph is an intersection graph of arithmetic progressions (dotted intervals). Coloring of dotted interval...
详细信息
We introduce a generalization of interval graphs, which we call Dotted Interval Graphs (DIG). A dotted interval graph is an intersection graph of arithmetic progressions (dotted intervals). Coloring of dotted interval graphs naturally arises in the context of high throughput genotyping. We study the properties of dotted interval graphs, with a focus on coloring. We show that any graph is a DIG, but that DIG(d) graphs, that is, DIGs in which the arithmetic progressions have a jump of at most d, form a strict hierarchy. We show that coloring DIG(d) graphs is NP-complete even for d = 2. For any fixed d, we provide a 5/6 d + o(d) approximation for the coloring of DIG(d) graphs. Finally, we show that finding the maximal clique in DIG(d) graphs is fixed parameter tractable in d.
We study budget constrained network upgrading problems. We are given an undirected edge-weighted graph G = (V, E), where node upsilon E V can be upgraded at a cost of c(upsilon). This upgrade reduces the weight of eac...
详细信息
We study budget constrained network upgrading problems. We are given an undirected edge-weighted graph G = (V, E), where node upsilon E V can be upgraded at a cost of c(upsilon). This upgrade reduces the weight of each edge incident on upsilon. The goal is to find a minimum cost set of nodes to be upgraded so that the resulting network has a minimum spanning tree of weight no more than a given budget D. The results obtained in the paper include 1. On the positive side, we provide a polynomial time approximation algorithm for the above upgrading problem when the difference between the maximum and minimum edge weights is bounded by a polynomial in n, the number of nodes in the graph. The solution produced by the algorithm satisfies the budget constraint, and the cost of the upgrading set produced by the algorithm is O(log n) times the minimum upgrading cost needed to obtain a spanning tree of weight at most D. 2. In contrast, we show that, unless N-O subset of or equal to DTIME(n(O)((log log n))), there can be no polynomial time approximation algorithm for the problem that produces a solution with upgrading cost at most alpha < In n times the optimal upgrading cost even if the budget can be violated by a factor f(n), for any polynomial time computable function f(rt). This result continues to hold, with f(n) = n(k) being any polynomial, even when the difference between the maximum and minimum edge weights is bounded by a polynomial in n. 3. Finally, we show that using a sample binary search over the set of admissible values, the dual problem can be solved with an appropriate performance guarantee, (C) 1999 Academic Press.
The Minimum Dominating Set (MDS) problem is a fundamental and challenging problem in distributed computing. While it is well known that minimum dominating sets cannot be well approximated locally on general graphs, in...
详细信息
The Minimum Dominating Set (MDS) problem is a fundamental and challenging problem in distributed computing. While it is well known that minimum dominating sets cannot be well approximated locally on general graphs, in recent years there has been much progress on computing good local approximations on sparse graphs and in particular on planar graphs. In this article, we study distributed and deterministic MDS approximation algorithms for graph classes beyond planar graphs. In particular, we show that existing approximation bounds for planar graphs can be lifted to bounded genus graphs and more general graphs, which we call locally embeddable graphs, and present (1) a local constant-time, constant-factor MDS approximation algorithm on locally embeddable graphs, and (2) a local O(log* n)-time (1+epsilon)-approximation scheme for any epsilon > 0 on graphs of bounded genus. Our main technical contribution is a new analysis of a slightly modified variant of an existing algorithm by Lenzen et al. [21]. Interestingly, unlike existing proofs for planar graphs, our analysis does not rely on direct topological arguments but on combinatorial density arguments only.
A comparative analysis of toroidal, compressional and vortical dipole strengths in the spherical Sm-144 and the deformed Sm-154 is performed within the random-phase approximation using a set of different Skyrme forces...
详细信息
A comparative analysis of toroidal, compressional and vortical dipole strengths in the spherical Sm-144 and the deformed Sm-154 is performed within the random-phase approximation using a set of different Skyrme forces. Isoscalar (T = 0), isovector (T = 1), and electromagnetic excitation channels are considered. The role of the nuclear convection j(con) and magnetization j(mag) currents is inspected. It is shown that the deformation leads to an appreciable redistribution of the strengths and causes a spectacular deformation splitting (exceeding 5 MeV) of the isoscalar compressional mode. When stepping from Sm-144 to Sm-154, we observe an increase of the toroidal, compression and vortical contributions in the low-energy region (often called pygmy resonance). The strength in this region seems to be an overlap of various excitation modes. The energy centroids of the strengths depend significantly on the isoscalar effective mass m(0). Skyrme forces with a large m(0) (typically m(0)/m approximate to 0.8-1) seem to be more suitable for the description of experimental data for the isoscalar giant dipole resonance.
This paper estimates free energy, average mutual information, and minimum mean square error (MMSE) of a linear model under two assumptions: 1) the source is generated by a Markov chain;2) the source is generated via a...
详细信息
This paper estimates free energy, average mutual information, and minimum mean square error (MMSE) of a linear model under two assumptions: 1) the source is generated by a Markov chain;2) the source is generated via a hidden Markov model. Our estimates are based on the replica method in statistical physics. We show that under the posterior mean estimator, the linear model with Markov sources or hidden Markov sources is decoupled into single-input AWGN channels with state information available at both encoder and decoder where the state distribution follows the left Perron-Frobenius eigenvector with unit Manhattan norm of the stochastic matrix of Markov chains. Numerical results show that the free energies and MSEs obtained via the replica method are closely approximate to their counterparts achieved by the Metropolis-Hastings algorithm or some well-known approximate message passing algorithms in the research literature.
In multisensor target tracking systems receiving out-of-sequence measurements (OOSMs) from local sensors is a common situation. In the last decade many algorithms have been proposed to update with an OOSM optimally or...
详细信息
In multisensor target tracking systems receiving out-of-sequence measurements (OOSMs) from local sensors is a common situation. In the last decade many algorithms have been proposed to update with an OOSM optimally or suboptimally. However, what one faces in the real world is the multiple OOSMs, which arrive at the fusion center in, generally, arbitrary orders, e. g., in succession or interleaved with in-sequence measurements. A straightforward approach to deal with this multi-OOSM problem is by sequentially applying a given OOSM algorithm;however, this simple solution does not guarantee the optimal update under the multi-OOSM scenario. The work presented here discusses the differences between the single-OOSM processing and the multi-OOSM processing, and presents the general solution to the multi-OOSM problem, which is called the complete in-sequence information (CISI) approach. Given an OOSM, in addition to updating the state at the most recent time, the CISI approach also updates the states between the OOSM time and the most recent time, including the state at the OOSM time. Three novel CISI methods are developed in this paper: the information filter-equivalent measurement (IF-EqM) method, the CISI fixed-point smoothing (CISI-FPS) method and the CISI fixed-interval smoothing (CISI-FIS) method. Numerical examples are given to illustrate the optimality of these CISI methods under various multi-OOSM scenarios.
Given an interval graph and integer , we consider the problem of finding a subgraph of size with a maximum number of induced edges, called densest k -subgraph problem in interval graphs. This problem is NP-hard even f...
详细信息
Given an interval graph and integer , we consider the problem of finding a subgraph of size with a maximum number of induced edges, called densest k -subgraph problem in interval graphs. This problem is NP-hard even for chordal graphs (Perl and Corneil in Discret Appl Math 9(1):27-39, 1984), and there is probably no PTAS for general graphs (Khot and Subhash in SIAM J Comput 36(4):1025-1071, 2006). However, the exact complexity status for interval graphs is a long-standing open problem (Perl and Corneil in Discret Appl Math 9(1):27-39, 1984), and the best known approximation result is a -approximation algorithm (Liazi et al. in Inf Process Lett 108(1):29-32, 2008). We shed light on the approximation complexity of finding a densest -subgraph in interval graphs by presenting a polynomial-time approximation scheme (PTAS), that is, we show that there is an -approximation algorithm for any , which is the first such approximation scheme for the densest -subgraph problem in an important graph class without any further restrictions.
We study the problem of augmenting a weighted graph by inserting edges of bounded total cost while minimizing the diameter of the augmented graph. Our main result is an FPT -approximation algorithm for the problem.
We study the problem of augmenting a weighted graph by inserting edges of bounded total cost while minimizing the diameter of the augmented graph. Our main result is an FPT -approximation algorithm for the problem.
The problem of simplifying a polygonal curve or chain is well studied and has many applications. The discrete Frechet distance is a useful similarity measure for curves, which has been utilized for many real-world app...
详细信息
The problem of simplifying a polygonal curve or chain is well studied and has many applications. The discrete Frechet distance is a useful similarity measure for curves, which has been utilized for many real-world applications. When the curves are huge, a simplification algorithm is needed in order to reduce running times. In this paper we adapt some of the techniques of Driemel and Har-Peled [5] (for the continuous Frechet distance) to obtain a universal approximate simplification of a given polygonal curve, under the discrete Frechet distance. (C) 2017 Elsevier B.V. All rights reserved.
The increasing availability of autonomous small-size Unmanned Aerial Vehicles (UAVs) has provided a promising way for data gathering from Wireless Sensor Networks (WSNs) with the advantages of high mobility, flexibili...
详细信息
The increasing availability of autonomous small-size Unmanned Aerial Vehicles (UAVs) has provided a promising way for data gathering from Wireless Sensor Networks (WSNs) with the advantages of high mobility, flexibility, and good speed. However, few works considered the situations that multiple UAVs are collaboratively used and the fine-grained trajectory plans of multiple UAVs are devised for collecting data from network including detailed traveling and hovering plans of them in the continuous space. In this paper, we investigate the problem of the Fine-grained Trajectory Plan for multi-UAVs (FTP), in which m UAVs are used to collect data from a given WSN, where m >= 1 . The problem entails not only to find the flight paths of multiple UAVs but also to design the detailed hovering and traveling plans on their paths for efficient data gathering from WSN. The objective of the problem is to minimize the maximum flight time of UAVs such that all sensory data of WSN is collected by the UAVs and transported to the base station. We first propose a mathematical model of the FTP problem and prove that the problem is NP-hard. To solve the FTP problem, we first study a special case of the FTP problem when m = 1, called FTP with Single UAV (FTPS) problem. Then we propose a constant-factor approximation algorithm for the FTPS problem. Based on the FTPS problem, an approximation algorithm for the general version of the FTP problem when m > 1 is further proposed, which can guarantee a constant factor of the optimal solution. Afterwards, the proposed algorithms are verified by extensive simulations.
暂无评论