We are given a set U of user points, a set S of sensors in a d-dimensional space R-d and a lower bound H. Each user point u is an element of U has a profit pi(u) and a penalty cost p(u). Each sensor s is an element of...
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ISBN:
(纸本)9783031207952;9783031207969
We are given a set U of user points, a set S of sensors in a d-dimensional space R-d and a lower bound H. Each user point u is an element of U has a profit pi(u) and a penalty cost p(u). Each sensor s is an element of S can adjust its power, and the cover range of sensors with power p(s) is a d-dimensional ball of radius r(s), where p(s) = r(s)(alpha) and alpha >= 1 is a constant. The goal of the H-prize-collecting power cover problem is to determine a power assignment such that the total profit of covered user points is at least H and the total power of sensors plus the total penalty cost of uncovered user points is minimized. First, we proved that this problem is NP-hard even when alpha = 1, and d = 1 and pi(u) = 0 for any u is an element of U. Then, by utilizing primal-dual and Lagrangian relaxation techniques, we present a (4 center dot 3(alpha-1) + epsilon)-approximation algorithm for any desired accuracy epsilon > 0.
A Wireless Sensor Network (WSN) is composed by a larger number of low-power sensor nodes to gather environmental information and forward those gathered information wirelessly to a base station. However, due to the lim...
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ISBN:
(纸本)9781509015405
A Wireless Sensor Network (WSN) is composed by a larger number of low-power sensor nodes to gather environmental information and forward those gathered information wirelessly to a base station. However, due to the limited communication range of sensor nodes, relay nodes need to be included in order to make the whole WSN connected. Relay nodes are typically more advanced and more expensive than sensor nodes. Therefore, developing strategies to deploy relay nodes effectively and minimize the number of relay nodes has always been a hot research topic, also known as the Steiner Tree Problem with Minimum number of Steiner Points (SMT-MSP), which is proved to be NP-hard by previous work. In this paper, we analyze and improve the 3-star approximation algorithm by reducing the time complexity from O(n(3)) to O(n log n) with identical performance ratio. Experiments are conducted to verify the correctness of the proposed algorithm.
Given two genomic maps G(1) and G(2) each represented as a sequence of n gene markers, the maximal strip recovery ( MSR) problem is to retain the maximum number of markers in both G(1) and G(2) such that the resultant...
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ISBN:
(纸本)9783642212048
Given two genomic maps G(1) and G(2) each represented as a sequence of n gene markers, the maximal strip recovery ( MSR) problem is to retain the maximum number of markers in both G(1) and G(2) such that the resultant subsequences, denoted as G(1)(*) and G(2)(*), can be partitioned into the same set of maximal strips, which are common substrings of length greater than or equal to two. The complementary maximal strip recovery (CMSR) problem has the complementary goal to delete the minimum number of markers. Both MSR and CMSR have been shown NP-hard and APX-complete, and they admit a 4-approximation and a 3-approximation respectively. In this paper, we present an improved 7/3-approximation algorithm for the CMSR problem, with its worst-case performance analysis done through a sequential amortization.
Broadcasting is an information dissemination problem in a connected network in which one node, called the originator, must distribute a message to all other nodes by placing a series of calls along the communication l...
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Broadcasting is an information dissemination problem in a connected network in which one node, called the originator, must distribute a message to all other nodes by placing a series of calls along the communication lines of the network. In every unit of time, the informed nodes aid the originator in distributing the message. Finding the broadcast time of any vertex in an arbitrary graph is NP-complete. The polynomial time solvability is shown only for certain graphs like trees, unicyclic graphs, tree of cycles, necklace graphs, fully connected trees and tree of cliques. In this paper we study the broadcast problem in k-path graphs. For any originator of the k-path graph we present a (4 - epsilon)-approximation algorithm in the worst case. The algorithm gives a better approximation ratio for some large classes of k-path graphs. Moreover, our algorithm generates the optimal broadcast time for some cases.
Dynamic time warping (DTW) is a widely used curve similarity measure. We present a simple and efficient (1 + is an element of)approximation algorithm for DTW between a pair of point sequences, say, P and Q, each of wh...
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ISBN:
(纸本)9781450345897
Dynamic time warping (DTW) is a widely used curve similarity measure. We present a simple and efficient (1 + is an element of)approximation algorithm for DTW between a pair of point sequences, say, P and Q, each of which is sampled from a curve. We prove that the running time of the algorithm is O (k(2) /is an element of n log sigma) for a pair of k-packed curves with a total of n points, assuming that the spreads of P and Q are bounded by sigma. The spread of a point set is the ratio of the maximum to the minimum pairwise distance, and a curve is called k-packed if the length of its intersection with any disk of radius r is at most kr. Although an algorithm with similar asymptotic time complexity was presented in [1], our algorithm is considerably simpler and more e ffi cient in practice. We have implemented our algorithm. Our experiments on both synthetic and real_world data sets show that it is an order of magnitude faster than the standard exact DP algorithm on point sequences of length 5,000 or more while keeping the approximation error within 5-10%. We demonstrate the e ffi cacy of our algorithm by using it in two applications | computing the k most similar trajectories to a query trajectory, and running the iterative closest point method for a pair of trajectories. We show that we can achieve 8-12 times speedup using our algorithm as a subroutine in these applications, without compromising much in accuracy.
Triple patterning lithography (TPL) is one of the major techniques for 14 nm technology node and beyond. This paper discusses TPL layout decomposition which maximizes objective value representing decomposition quality...
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ISBN:
(纸本)9783319130750;9783319130743
Triple patterning lithography (TPL) is one of the major techniques for 14 nm technology node and beyond. This paper discusses TPL layout decomposition which maximizes objective value representing decomposition quality. We introduce a maximization problem of the weighted sum of resolved conflicts and unused stitch candidates. We propose a polynomial time (7/9)-approximation algorithm based on positive semidefinite relaxation and randomized rounding procedure. Our algorithm returns a decomposition such that the expectation of the corresponding objective value is at least (7/9) times the optimal value even in the worst case problem instance. To our knowledge, the result is the first approximation algorithm with a constant approximation ratio for TPL.
Determination of Ribonucleic Acid structure is challenging, in order to optimize the RNA pseudoknotted structure, the paper investigates the computational problem and complexity of predicting RNA structure. A new comp...
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ISBN:
(纸本)9781479913329;9781479940998
Determination of Ribonucleic Acid structure is challenging, in order to optimize the RNA pseudoknotted structure, the paper investigates the computational problem and complexity of predicting RNA structure. A new computational method and model with minimum free energy are adopted to predict RNA structure. The main contribution of the paper is to achieves an efficient approximation algorithm for finding RNA pseudoknotted structure and nested structures. We have compared with other algorithms in time complexity and space complexity, the approximation algorithm takes O(n~3) time and O(n~2) space, where n is the length of the RNA sequences. The experimental tests for a large database of RNA show that the algorithm is more exact and effective than the algorithms, the algorithm can predict arbitrary pseudoknots, and improve the a predicting accuracy.
We consider the stochastic version of the facility location problem with service installation *** the primal-dual technique,we obtain a 7-approximation algorithm.
We consider the stochastic version of the facility location problem with service installation *** the primal-dual technique,we obtain a 7-approximation algorithm.
We consider the problem of minimizing the makespan(Cmax) on m identical parallel batch processing machines. The batch processing machine can process up to B jobs simultaneously. The jobs that are processed together fo...
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We consider the problem of minimizing the makespan(Cmax) on m identical parallel batch processing machines. The batch processing machine can process up to B jobs simultaneously. The jobs that are processed together form a batch, and all jobs in a batch start and complete at the same time. For a batch of jobs, the processing time of the batch is equal to the largest processing time among the jobs in the batch. In this paper, we design a fully polynomial time approximation scheme (FPTAS) to solve the bounded identical parallel batch scheduling problem Pm |B < n|Cmax when the number of identical parallel batch processing machines m is constant.
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