The haplotype inference problem (HIP) asks to find a set of haplotypes which resolve a given set of genotypes. This problem is important in practical fields such as the investigation of diseases or other types of gene...
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The haplotype inference problem (HIP) asks to find a set of haplotypes which resolve a given set of genotypes. This problem is important in practical fields such as the investigation of diseases or other types of genetic mutations. In order to find the haplotypes which are as close as possible to the real set of haplotypes that comprise the genotypes, two models have been suggested which are by now well-studied: The perfect phylogeny model and the pure parsimony model. All known algorithms up till now for haplotype inference may find haplotypes that are not necessarily plausible, i.e., very rare haplotypes or haplotypes that were never observed in the population. In order to overcome this disadvantage, we study in this paper, a new constrained version of HIP under the above-mentioned models. In this new version, a pool of plausible haplotypes (H) over tilde is given together with the set of genotypes G, and the goal is to find a subset H subset of (H) over tilde that resolves G. For constrained perfect phylogeny haplotyping (CPPH), we provide initial insights and polynomial-time algorithms for some restricted cases of the problem. For constrained parsimony haplotyping (CPH), we show that the problem is fixed parameter tractable when parameterized by the size of the solution set of haplotypes.
The problem of computing minimum distortion embeddings of a given graph into a line (path) was introduced in 2004 and has quickly attracted significant attention with subsequent results appearing at recent STOC and SO...
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The problem of computing minimum distortion embeddings of a given graph into a line (path) was introduced in 2004 and has quickly attracted significant attention with subsequent results appearing at recent STOC and SODA conferences. So far, all such results concern approximation algorithms or exponential-time exact algorithms. We give the first polynomial-time algorithms for computing minimum distortion embeddings of graphs into a path when the input graphs belong to specific graph classes. In particular, we solve this problem in polynomialtime for bipartite permutation graphs and threshold graphs. For both graph classes, the distortion can be arbitrarily large. The graphs that we consider are unweighted. (C) 2011 Elsevier B.V. All rights reserved.
It is well known that general 0-1 programming problems are NP-Complete and their optimal solutions cannot be found with polynomial-time algorithms unless P=NP. In this paper, we identify a specific class of 0-1 progra...
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It is well known that general 0-1 programming problems are NP-Complete and their optimal solutions cannot be found with polynomial-time algorithms unless P=NP. In this paper, we identify a specific class of 0-1 programming problems that is polynomially solvable, and propose two polynomial-time algorithms to find its optimal solutions. This class of 0-1 programming problems commits to a wide range of real-world industrial applications. We provide an instance of representative in the field of supply chain management.
We consider the problem of energy-efficient transmission in multi-flow multihop cooperative wireless networks. Although the performance gains of cooperative approaches are well known, the combinatorial nature of these...
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ISBN:
(纸本)9781424492688
We consider the problem of energy-efficient transmission in multi-flow multihop cooperative wireless networks. Although the performance gains of cooperative approaches are well known, the combinatorial nature of these schemes makes it difficult to design efficient polynomial-time algorithms for joint routing, scheduling and power control. This becomes more so when there is more than one flow in the network. It has been conjectured by many authors, in the literature, that the multiflow problem in cooperative networks is an NP-hard problem. In this paper, we formulate the problem, as a combinatorial optimization problem, for a general setting of k-flows, and formally prove that the problem not only NP-hard but it is o(n(1/7-epsilon)) inapproxmiable. To our knowledge, the results in this paper provide the first such inapproxmiablity proof in the context of multiflow cooperative wireless networks. We further prove that for a special case of k = 1 the solution is a simple path, and offer a polynomialtime algorithm for jointly optimizing routing, scheduling and power control.
This paper focuses on single machine scheduling subject to inventory constraints. Jobs either add items to an inventory or remove items from that inventory. Jobs that have to remove items cannot be processed if the re...
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This paper focuses on single machine scheduling subject to inventory constraints. Jobs either add items to an inventory or remove items from that inventory. Jobs that have to remove items cannot be processed if the required number of items is not available. We consider scheduling problems on a single machine with the minimization of the total weighted completion time, the maximum lateness, and the number of tardy jobs, respectively, as objective and determine their computational complexity. Since the general versions of our problems turn out to be strongly NP-hard, we consider special cases by assuming that different jobs have certain parameter values in common. We determine the computational complexity for all special cases when the objective is either to minimize total completion time or to minimize maximum lateness and for several special cases when the objective is either to minimize total weighted completion time or to minimize the number of tardy jobs. (C) 2010 Elsevier BM. All rights reserved.
We consider a new model of time-dependent scheduling. A set of deteriorating jobs has to be processed on a single machine which is available starting from a non-zero time. The processing times of some jobs from this s...
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We consider a new model of time-dependent scheduling. A set of deteriorating jobs has to be processed on a single machine which is available starting from a non-zero time. The processing times of some jobs from this set are constant, while other ones are either proportional or linear functions of the job starting times. The applied criteria of schedule optimality include the maximum completion time, the total completion time, the total weighted completion time, the maximum lateness and the number of tardy jobs. We delineate a sharp boundary between computationally easy and difficult problems, showing polynomially solvable and NP-hard cases. (C) 2010 Elsevier Inc. All rights reserved.
This paper deals with due date assignment and just-in-time scheduling for single machine and parallel machine problems with equal-size jobs where the objective is to minimize the total weighted earliness-tardiness and...
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This paper deals with due date assignment and just-in-time scheduling for single machine and parallel machine problems with equal-size jobs where the objective is to minimize the total weighted earliness-tardiness and due date cost. These two problems, but with a common due date to be calculated, were shown to be polynomially solvable in O(n(4)) time. We first show that this complexity can be reduced to O(n(3)) by modeling the single machine scheduling problem as an assignment problem without necessary due date enumeration. We next prove that the general case with identical parallel machines and a given set of assignable due dates where the cardinality of this set is bounded by a constant number is still polynomially solvable. (C) 2010 Elsevier B.V. All rights reserved.
In a traditional wakeup scheduling, sensor nodes start up numerous times to communicate in a period, thus consuming extra energy due to state transitions (e.g. from the sleep state to the active state). In this paper,...
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ISBN:
(纸本)9781424456383
In a traditional wakeup scheduling, sensor nodes start up numerous times to communicate in a period, thus consuming extra energy due to state transitions (e.g. from the sleep state to the active state). In this paper, we address a novel wakeup scheduling problem called compact wakeup scheduling, in which a node needs to wake up only once to communicate bidirectionally with all its neighbors. However, not all communication graphs have valid compact wakeup schedulings, and thus we focus on tree and grid topologies that have valid compact wakeup schedulings. We propose polynomial-time algorithms using the optimum number of time slots in a period for tree and grid topologies.
This paper deals with the estimation of returns to scale (RTS) in free disposal hull (FDH) models and provides some stability intervals for preserving the RTS classification. It has been shown that the proposed stabil...
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This paper deals with the estimation of returns to scale (RTS) in free disposal hull (FDH) models and provides some stability intervals for preserving the RTS classification. It has been shown that the proposed stability intervals can be obtained via a polynomial-time algorithm based on the calculation of certain ratios of inputs and outputs, without solving any mathematical programming problem. The results of the study have been proved via some lemmas and theorems and have been illustrated by numerical examples and a real application. (c) 2008 Elsevier B.V. All rights reserved.
We consider the problem of preemptively scheduling n independent jobs on m parallel machines so as to minimize the makespan. Each job J(j) has a release time r(j) and it can only be processed on a subset of machines M...
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We consider the problem of preemptively scheduling n independent jobs on m parallel machines so as to minimize the makespan. Each job J(j) has a release time r(j) and it can only be processed on a subset of machines M-j. The machines are linearly ordered. Each job J(j) has a machine index a(j) such that M-j = {M-aj, Maj+1, ... , M-m}. We first show that there is no 1-competitive online algorithm for this problem. We then give an offline algorithm with a running time of O(nk logP + mnk(2) + m(3)k), where k is the number of distinct release times and P is the total processing time of all jobs. (C) 2009 Elsevier B.V. All rights reserved.
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