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Scheduling on Unrelated Machines under TreeLike Precedence Constraints ∗
"... We present polylogarithmic approximations for the RprecCmax and Rprec  � j wjCj problems, when the precedence constraints are “treelike ” i.e., when the undirected graph underlying the precedences is a forest. These are the first nontrivial generalizations of the job shop scheduling problem to ..."
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We present polylogarithmic approximations for the RprecCmax and Rprec  � j wjCj problems, when the precedence constraints are “treelike ” i.e., when the undirected graph underlying the precedences is a forest. These are the first nontrivial generalizations of the job shop scheduling problem
Scheduling on Unrelated Machines under TreeLike Precedence Constraints
"... We present polylogarithmic approximations for the RprecCmax and Rprec  � j wjCj problems, when the precedence constraints are “treelike ” i.e., when the undirected graph underlying the precedences is a forest. These are the first nontrivial generalizations of the job shop scheduling problem to ..."
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Cited by 8 (1 self)
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We present polylogarithmic approximations for the RprecCmax and Rprec  � j wjCj problems, when the precedence constraints are “treelike ” i.e., when the undirected graph underlying the precedences is a forest. These are the first nontrivial generalizations of the job shop scheduling problem
Optimal Parallel Algorithms for Two Processor Scheduling with Tree Precedence Constraints
, 1995
"... Consider the problem of finding a minimum length schedule for n unit execution time tasks on m processors with treelike precedence constraints. A sequential algorithm can solve this problem in linear time. The fastest known parallel algorithm needs O(log n) time using n² processors. For the case m ..."
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Consider the problem of finding a minimum length schedule for n unit execution time tasks on m processors with treelike precedence constraints. A sequential algorithm can solve this problem in linear time. The fastest known parallel algorithm needs O(log n) time using n² processors. For the case m
Regression Shrinkage and Selection Via the Lasso
 JOURNAL OF THE ROYAL STATISTICAL SOCIETY, SERIES B
, 1994
"... We propose a new method for estimation in linear models. The "lasso" minimizes the residual sum of squares subject to the sum of the absolute value of the coefficients being less than a constant. Because of the nature of this constraint it tends to produce some coefficients that are exactl ..."
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Cited by 4191 (49 self)
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We propose a new method for estimation in linear models. The "lasso" minimizes the residual sum of squares subject to the sum of the absolute value of the coefficients being less than a constant. Because of the nature of this constraint it tends to produce some coefficients
Scheduling a Single Machine with Resource Dependent Release Times
, 2000
"... We consider the problem of scheduling n jobs on a single machine to minimize makespan. Release times and precedence constraints between the jobs are imposed. The release times are not xed but depend on an additional resource expenditure. More precisely, the release time of each job is a linear func ..."
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function of the amount of resource alotted to this job. The total available amount of the resource is restricted. It is shown that even very special cases of this problem are NPhard. For the general case of our problem, we give a heuristic with performance guarantee 2. For the problem with treelike
Batch Coloring Treelike Graphs
"... Batch scheduling of conflicting jobs is modeled by batch coloring of a graph. Given an undirected graph and the number of colors required by each vertex, we need to find a proper batch coloring of the graph, i.e., partition the vertices to batches which are independent sets, and to assign to each ba ..."
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solutions can be obtained efficiently. In this paper we give the first polynomial time approximation schemes for batch sum coloring on treelike graphs, as well as for planar graphs. For the maxcoloring problem, we improve upon previous results for several classes of treelike graphs, as well
Scheduling UnitTime Operation Jobs On Identical Parallel Machines And In A Flow Shop: Complexity And Correlation
, 1998
"... . This paper considers the complexity and the correlation of scheduling unittime jobs on identical parallel machines and unittime flowshop scheduling under precedence constraints. It is shown that, in the case of chainlike precedence constraints, the nonpreemptive parallelmachines problem and t ..."
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Cited by 1 (1 self)
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, whereas the related flowshop problem remains so only in the twomachine case. For general precedence constraints and treelike precedence constraints with different release dates of jobs, it is shown a polynomialtime reduction from the preemptive parallelmachines problems to the flowshop problems
Parallel machine scheduling with uncertain communication delays
 2003, RAIRO Operations Research
"... Abstract. This paper is concerned with scheduling when the data are not fully known before the execution. In that case computing a complete schedule offline with estimated data may lead to poor performances. Some flexibility must be added to the scheduling process. We propose to start from a parti ..."
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Cited by 3 (0 self)
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, link failures,... may occur at execution time. Hence the processor assignment and a partial sequencing on each processor are determined offline. Some theoretical results for treelike precedence constraints and an experimental study show the interest of this approach compared with fully online scheduling.
A Combinatorial Analysis of TreeLike Sentences
, 2015
"... A sentence over a finite alphabet A, is a finite sequence of nonempty words over A. More generally, we define a graphical sentence over A by attaching a nonempty word over A to each arrow and each loop of a connected directed graph (digraph, for short). Each word is written according to the direct ..."
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, in the context of combinatorial species and Pólya theories, to analyze parameters in classes of treelike sentences. These are graphical sentences constructed on treelike digraphs.
FACTOR MODELS ON LOCALLY TREELIKE GRAPHS
, 2011
"... We consider homogeneous factor models on uniformly sparse graph sequences converging locally to a (unimodular) random tree T, and study the existence of the free energy density φ, the limit of the logpartition function divided by the number of vertices n as n tends to infinity. We provide a new i ..."
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Cited by 7 (2 self)
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We consider homogeneous factor models on uniformly sparse graph sequences converging locally to a (unimodular) random tree T, and study the existence of the free energy density φ, the limit of the logpartition function divided by the number of vertices n as n tends to infinity. We provide a new
Results 1  10
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714,591