Genome Rearrangements affect large stretches of genomes during evolution. One of the most studied genome rearrangement is the transposition, which occurs when a sequence of genes is moved to another position inside th...
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ISBN:
(纸本)9783030422660;9783030422653
Genome Rearrangements affect large stretches of genomes during evolution. One of the most studied genome rearrangement is the transposition, which occurs when a sequence of genes is moved to another position inside the genome. Mathematical models have been used to estimate the evolutionary distance between two different genomes based on genome rearrangements. However, many of these models have focused only on the (order of the) genes of a genome, disregarding other important elements in it. Recently, researchers have shown that considering existing regions between each pair of genes, called intergenic regions, can enhance the distance estimation in realistic data. In this work, we study the transposition distance between two genomes, but we also consider intergenic regions, a problem we name Sorting Permutations by Intergenic Transpositions (SbIT). We show that this problem is NP-hard and propose a 3.5-approximation algorithm for it.
Proposed algorithms for calculating the shortest paths such as Dijikstra and Flowd-Warshall's algorithms are limited to small networks due to computational complexity and cost. We propose an efficient and a more a...
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Proposed algorithms for calculating the shortest paths such as Dijikstra and Flowd-Warshall's algorithms are limited to small networks due to computational complexity and cost. We propose an efficient and a more accurate approximation algorithm that is applicable to large scale networks. Our algorithm iteratively constructs levels of hierarchical networks by a node condensing procedure to construct hierarchical graphs until threshold. The shortest paths between nodes in the original network are approximated by considering their corresponding shortest paths in the highest hierarchy. Experiments on real life data show that our algorithm records high efficiency and accuracy compared with other algorithms.
In this paper, we introduce a squared metric k-facility location problem (SM-k-FLP) which is a generalization of the squared metric facility location problem (SMFLP) and k-facility location problem (k-FLP). In the SM-...
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ISBN:
(纸本)9783319711508;9783319711492
In this paper, we introduce a squared metric k-facility location problem (SM-k-FLP) which is a generalization of the squared metric facility location problem (SMFLP) and k-facility location problem (k-FLP). In the SM-k-FLP, we are given a client set C and a facility set F from a metric space, a facility opening cost f(i) >= 0 for each i is an element of F, and an integer k. The goal is to open a facility subset F subset of F with vertical bar F vertical bar <= k and to connect each client to the nearest open facility such that the total cost (including facility opening cost and the sum of squares of distances) is minimized. Using local search and scaling techniques, we offer a constant approximation algorithm for the SM-k-FLP.
In this paper, we introduce a model of distributionally robust facility location problem (DRFLP) under moment constraints up to the second order. We show, via duality theory of moment problems, that the linear relaxat...
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ISBN:
(纸本)9783319083773;9783319083766
In this paper, we introduce a model of distributionally robust facility location problem (DRFLP) under moment constraints up to the second order. We show, via duality theory of moment problems, that the linear relaxation of the DRFLP is equivalent to that of the standard uncapacitated facility location problem (UFLP). Consequently, any LP-based approximation algorithm for the UFLP implies an approximation algorithm for the DRFLP with the same approximation ratio.
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.
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.
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.
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