Scaffolding is one of the main stages in genome assembly. During this stage, we want to merge contigs assembled from the paired-end reads into bigger chains called scaffolds. For this purpose, the following graph-theo...
详细信息
Scaffolding is one of the main stages in genome assembly. During this stage, we want to merge contigs assembled from the paired-end reads into bigger chains called scaffolds. For this purpose, the following graph-theoretical problem has been proposed: Given an edge-weighted complete graph G and a perfect matching D of G, we wish to find a Hamiltonian path P in G such that all edges of D appear in P and the total weight of edges in P but not in D is maximized. This problem is NP-hard and the previously best polynomial-time approximation algorithm for it achieves a ratio of 1/2. In this paper, we design a new polynomial-time approximation algorithm achieving a ratio of 5-5 is an element of/9-8 is an element of for any constant 0 < is an element of < 1. Several generalizations of the problem have also been introduced in the literature and we present polynomial-time approximation algorithms for them that achieve better approximation ratios than the previous bests. In particular, one of the algorithms answers an open question. (C) 2017 Elsevier B.V. All rights reserved.
In this work, we are interested in the problem of task scheduling on large-scale data-intensive computing systems. In order to achieve good performance, one must construct not only good task schedules but also good da...
详细信息
In this work, we are interested in the problem of task scheduling on large-scale data-intensive computing systems. In order to achieve good performance, one must construct not only good task schedules but also good data allocation across nodes on the system, since before a task can be executed, it must have access to data distributed on the system. In this article, we present a general formulation of a static problem that combines both scheduling and replication problems in data-intensive distributed systems. We show that this problem does not admit an approximation algorithm. However, considering a restricted version of the problem that considers some practical constraints, an approximation algorithm can be designed. From a practical perspective, we introduce a novel heuristic for the problem that is based on nodes clustering. We compare the heuristic with two adapted approaches from other works in the literature by computational simulations using an extensive set of instances based on real computer grids. We show that our heuristic often obtains the best solutions and also runs faster than other approaches.
Motivated by the Steiner tree problem with minimum number of Steiner points and bounded edge-length in [4], we consider the problem of constructing specific subgraph with minimum number of length-bounded stock pieces ...
详细信息
Motivated by the Steiner tree problem with minimum number of Steiner points and bounded edge-length in [4], we consider the problem of constructing specific subgraph with minimum number of length-bounded stock pieces (CSS-MSP, for short), which is defined as follows. In some constructing specific subgraph problem Q (CSS, for short), the objective is to choose a minimum-length subset of edges, such that these edges form a specific subgraph (such as a spanning tree or a Steiner tree). In the CSS-MSP problem Q', these edges are further required to be cut from some stock pieces of length L, and the new objective, however, is to minimize the number of stock pieces of length L to construct all edges in such a specific subgraph. We obtain two main results. (1) Whenever the CSS problem Q can be approximated by an alpha-approximation algorithm (alpha >= 1) (for the case alpha = 1, the CSS problem Q is solved optimally by a polynomial-time exact algorithm), we design two approximation algorithms with performance ratios 2 alpha and 7 alpha/4 to solve the CSS-MSP problem Q';(2) In addition, when the problem Q is to find a minimum spanning tree, we present a 3/2-approximation algorithm and an APTAS to solve the problem Q' of constructing spanning tree with minimum number of length-bounded stock pieces. (C) 2018 Elsevier B.V. All rights reserved.
We present improved approximation algorithms in stochastic optimization. We prove that the multistage stochastic versions of covering integer programs (such as set cover and vertex cover) admit essentially the same ap...
详细信息
We present improved approximation algorithms in stochastic optimization. We prove that the multistage stochastic versions of covering integer programs (such as set cover and vertex cover) admit essentially the same approximation algorithms as their standard (nonstochastic) counterparts;this improves upon work of Swamy and Shmoys which shows an approximability that depends multiplicatively on the number of stages. We also present approximation algorithms for facility location and some of its variants in the 2-stage recourse model, improving on previous approximation guarantees. We give a 2.2975-approximation algorithm in the standard polynomial-scenario model and an algorithm with an expected per-scenario 2.4957-approximation guarantee, which is applicable to the more general black-box distribution model.
The Euler genus of a graph is a fundamental and well-studied parameter in graph theory and topology. Computing it has been shown to be NP-hard by Thomassen [J. algorithms, 10 (1989), pp. 568-576;T. Combin. Theory, Ser...
详细信息
The Euler genus of a graph is a fundamental and well-studied parameter in graph theory and topology. Computing it has been shown to be NP-hard by Thomassen [J. algorithms, 10 (1989), pp. 568-576;T. Combin. Theory, Ser. B, 57 (1993), pp. 196-206], and it is known to be fixed-parameter tractable. However, the approximability of the Euler genus is wide open. While the existence of an O(1)-approximation is not ruled out, only an O(Vh)-approximation [J. Chen, S. P. Kanchi, and A. Kanevsky, Inform. Process. Lett., 61 (1997), pp. 317-322] is known even in bounded-degree graphs. In this paper we give a polynomial-time algorithm which, given a bounded degree graph of Euler genus g, computes a drawing in a surface of Euler genus go(1) "logo(1) n. Combined with the upper bound from [J. Chen, S. P. Kanchi, and A. Kanevsky, Inform. Process. Lett., 61 (1997), pp. 317-322], our result also implies a 0(n1/2 ')-approximation for some constant a > 0. Using our algorithm for approximating the Euler genus as a subroutine, we obtain, in a uniform fashion, algorithms with approximation ratios of the form OPTc)(1) "logo(1) n for several related problems on bounded-degree graphs. These include the problems of orientable genus, crossing number, and planar edge and vertex deletion. Our algorithm and proof of correctness for the crossing number problem are simpler compared to the long and difficult proof in the recent breakthrough by Chuzhoy [Proceedings of the ACM Symposium on Theory of Computing, 2011, pp. 303-312], while essentially obtaining a qualitatively similar result. For planar edge and vertex deletion problems our results are the first to obtain a bound of the form poly(OPT, log n). We also highlight some further applications of our results in the design of algorithms for graphs with small genus. Many such algorithms require that a drawing of the graph is given as part of the input. Our results imply that in several interesting cases, we can implement such algorithms even when the
In this paper, we consider k-echelon extensions of the deterministic one warehouse multi-retailer problem. We give constant factor approximation algorithms for some of these extensions when k is fixed. We focus first ...
详细信息
In this paper, we consider k-echelon extensions of the deterministic one warehouse multi-retailer problem. We give constant factor approximation algorithms for some of these extensions when k is fixed. We focus first on the case without backorders and we give a -approximation algorithm under general assumptions on the evolution of the holding costs as products move toward the final customers. We then improve this result to a k-approximation when the holding costs are monotonically non-increasing or non-decreasing (which is a natural situation in practice). Finally we address problems with backorders: we give a 3-approximation for the one-warehouse multi-retailer problem with backlog and a k-approximation algorithm for the k-level Joint Replenishment Problem with backlog (a variant where inventory can only be kept at the final retailers). Ours results are the first constant approximation algorithms for those problems. In addition, we demonstrate the potential of our approach on a practical case. Our preliminary experiments show that the average optimality gap is around 15%.
Minimum Diameter Color Spanning Set (MDCSS) on a given set of colored points is the problem of selecting one point from each color such that the diameter of the selected points gets minimized. In this paper, we presen...
详细信息
Minimum Diameter Color Spanning Set (MDCSS) on a given set of colored points is the problem of selecting one point from each color such that the diameter of the selected points gets minimized. In this paper, we present some approximation algorithms and show some results on approximability of this problem in low and high dimensions. (C) 2018 Published by Elsevier B.V.
Genome rearrangements are events that affect large portions of a genome. When using the rearrangement distance to compare two genomes, one wants to find a minimum cost sequence of rearrangements that transforms one in...
详细信息
Genome rearrangements are events that affect large portions of a genome. When using the rearrangement distance to compare two genomes, one wants to find a minimum cost sequence of rearrangements that transforms one into another. Since we represent genomes as permutations, we can reduce this problem to the problem of sorting a permutation with a minimum cost sequence of rearrangements. In the traditional approach, we consider that all rearrangements are equally likely to occur and we set a unitary cost for all rearrangements. However, there are two variations of the problem motivated by the observation that rearrangements involving large segments of a genome rarely occur. The first variation adds a restriction to the rearrangement's length. The second variation uses a cost function based on the rearrangement's length. In this work, we present approximation algorithms for five problems combining both variations, that is, problems with a length-limit restriction and a cost function based on the rearrangement's length.
Today is an era where multiprocessor technology plays a major role in designs of modern computer architecture. While multiprocessor systems offer extra computing power, it also opens a new range of opportunities to im...
详细信息
Today is an era where multiprocessor technology plays a major role in designs of modern computer architecture. While multiprocessor systems offer extra computing power, it also opens a new range of opportunities to improve fault-robustness. This paper focuses on a problem of achieving fault-tolerance using replications in real-time, multiprocessor systems. In the problem, multiple replicas, or copies, of a computing task are executed on distinct processors to resist potential processor failures and computing faults. Two greedy, approximation heuristics, named Worst Fit Increasing K-Replication and First Fit Increasing K-Replication, are studied to maximise the number of real-time tasks assigned on a system with identical processors, respecting to the tasks' replicating and timely requirements. Worst case performance is analysed by using an approximation ratio between the algorithms and an optimal solution. We mathematically prove that the ratios of using both algorithms are infinitely close to 2. Simulations are performed on a large set of testing cases which can be used to bring to light the average performance of using the algorithms in practice. The results show that both heuristic algorithms provide simple but fast and effective solutions to solve the problem. [GRAPHICS] Assigning real-time tasks to a multiprocessor system with replications.
We propose a block successive convex approximation algorithm for large-scale nonsmooth nonconvex optimization problems. It is suitable for problems where the dimension exceeds the memory and/or the processing capabili...
详细信息
ISBN:
(纸本)9781728143002
We propose a block successive convex approximation algorithm for large-scale nonsmooth nonconvex optimization problems. It is suitable for problems where the dimension exceeds the memory and/or the processing capability of the existing hardware. The proposed algorithm partitions the whole set of variables into blocks which are updated sequentially. At each iteration, a particular block variable is selected and updated by solving an approximation subproblem with respect to that block variable only. The proposed algorithm has several attractive features, namely, i) high flexibility, as the approximation function only needs to be strictly convex and it does not have to be a global upper bound of the original function;ii) fast convergence, as the approximation function can be designed to exploit the problem structure at hand and the stepsize is calculated by the line search;iii) low complexity, as the line search scheme is carried out over a properly constructed differentiable function;iv) guaranteed convergence to a stationary point, even when the objective function does not have a Lipschitz continuous gradient. These features are illustrated by an application in network anomaly detection.
暂无评论