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10
Scheduling Hard RealTime Systems: A Review
, 1991
"... Recent results in the application of... this paper. The review takes the form of an analysis of the problems presented by different application requirements and characteristics. Issues covered include uniprocessor and multiprocessor systems, periodic and aperiodic processes, static and dynamic algor ..."
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Cited by 48 (7 self)
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Recent results in the application of... this paper. The review takes the form of an analysis of the problems presented by different application requirements and characteristics. Issues covered include uniprocessor and multiprocessor systems, periodic and aperiodic processes, static and dynamic algorithms, transient overloads and resource usage. Protocols that limit and reduce blocking are discussed. Considerations are also given to scheduling Ada tasks.
Biobjective approximation scheme for makespan and reliability optimization on uniform parallel machines
 EUROPAR
, 2008
"... ..."
Nonlinear matroid optimization and experimental design
 SIAM JOURNAL ON DISCRETE MATHEMATICS
, 2008
"... We study the problem of optimizing nonlinear objective functions over matroids presented by oracles or explicitly. Such functions can be interpreted as the balancing of multicriteria optimization. We provide a combinatorial polynomial time algorithm for arbitrary oraclepresented matroids, that mak ..."
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Cited by 9 (7 self)
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We study the problem of optimizing nonlinear objective functions over matroids presented by oracles or explicitly. Such functions can be interpreted as the balancing of multicriteria optimization. We provide a combinatorial polynomial time algorithm for arbitrary oraclepresented matroids, that makes repeated use of matroid intersection, and an algebraic algorithm for vectorial matroids. Our work is partly motivated by applications to minimumaberration modelfitting in experimental design in statistics, which we discuss and demonstrate in detail.
Toward Maximizing the Quality of Results of Dependent Tasks Computed Unreliably ⋆
"... Abstract. This paper studies the problem of maximizing the number of correct results of dependent tasks computed unreliably. We consider a distributed system composed of a reliable server that coordinates the computation of a massive number of unreliable workers. Any worker computes correctly with p ..."
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Cited by 8 (2 self)
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Abstract. This paper studies the problem of maximizing the number of correct results of dependent tasks computed unreliably. We consider a distributed system composed of a reliable server that coordinates the computation of a massive number of unreliable workers. Any worker computes correctly with probability p<1. Any incorrectly computed task corrupts all dependent tasks. The goal is to determine which tasks should be computed by the (reliable) server and which by the (unreliable) workers, and when, so as to maximize the expected number of correct results, under a constraint d on the computation time. This problem is motivated by distributed computing applications that persist partial results of computations for future use in other computations, and want to ensure that the persisted results are of high quality. We show that this optimization problem is NPhard. Then we study optimal scheduling solutions for the mesh with the tightest deadline. We present combinatorial arguments that describe all optimal solutions for two ranges of values of worker reliability p, whenp is close to zero and when p is close to one.
On the Solitaire Cone and Its Relationship to MultiCommodity Flows
 PREPRINT CAMS 142 ECOLE DES HAUTES ETUDES EN SCIENCES SOCIALES
, 2001
"... The classical game of Peg Solitaire has uncertain origins, but was certainly popular by the time of Louis XIV, and was described by Leibniz in 1710. The modern mathematical study of the game dates to the 1960s, when the solitaire cone was first described by Boardman and Conway. Valid inequalities ov ..."
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Cited by 7 (3 self)
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The classical game of Peg Solitaire has uncertain origins, but was certainly popular by the time of Louis XIV, and was described by Leibniz in 1710. The modern mathematical study of the game dates to the 1960s, when the solitaire cone was first described by Boardman and Conway. Valid inequalities over this cone, known as pagoda functions, were used to show the infeasibility of various peg games. In this paper we study the extremal structure of solitaire cones for a variety of boards, and relate their structure to the well studied metric cone. In particular we give: 1. an equivalence between the multicommodity flow problem with associated dual metric cone and a generalized peg game with associated solitaire cone; 2. a related NPcompleteness result; 3. a method of generating large classes of facets; 4. a complete characterization of 01 facets; 5. exponential upper and lower bounds (in the dimension) on the number of facets; 6. results on the number of facets, incidence and adjacency relationships and diameter for small rectangular, toric and triangular boards; 7. a complete characterization of the adjacency of extreme rays, diameter, number of 2faces and edge connectivity for rectangular toric boards.
Solitaire Cones
 Discrete Applied Mathematics
, 1996
"... The classical game of Peg Solitaire has uncertain origins, but was certainly popular by the time of Louis XIV, and was described by Leibniz in 1710. The modern mathematical study of the game dates to the 1960s, when the solitaire cone was first described by Boardman and Conway. Valid inequalities o ..."
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Cited by 5 (0 self)
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The classical game of Peg Solitaire has uncertain origins, but was certainly popular by the time of Louis XIV, and was described by Leibniz in 1710. The modern mathematical study of the game dates to the 1960s, when the solitaire cone was first described by Boardman and Conway. Valid inequalities over this cone, known as pagoda functions, were used to show the infeasibility of various peg games. In this paper we study the extremal structure of solitaire cones for a variety of boards, and relate their structure to the well studied metric cone. In particular we give: 1. an equivalence between the multicommodity flow problem with associated dual metric cone and a generalized peg game with associated solitaire cone; 2. a related NPcompleteness result; 3. a method of generating large classes of facets; 4. a complete characterization of 01 facets; 5. exponential upper and lower bounds (in the dimension) on the number of facets; 6. results on the number of facets, incidence, adjacency and ...
Convex Discrete Optimization
"... We develop an algorithmic theory of convex optimization over discrete sets. Using a combination of algebraic and geometric tools we are able to provide polynomial time algorithms for solving broad classes of convex combinatorial optimization problems and convex integer programming problems in variab ..."
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Cited by 1 (0 self)
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We develop an algorithmic theory of convex optimization over discrete sets. Using a combination of algebraic and geometric tools we are able to provide polynomial time algorithms for solving broad classes of convex combinatorial optimization problems and convex integer programming problems in variable dimension. We discuss some of the many applications of this theory including to quadratic programming, matroids, bin packing and cuttingstock problems, vector partitioning and clustering, multiway transportation problems, and privacy and confidential statistical data disclosure. Highlights of our work include a strongly polynomial time algorithm for convex and linear combinatorial optimization over any family presented by a membership oracle when the underlying polytope has few edgedirections; a new theory of sotermed nfold integer programming, yielding polynomial time solution of important and natural classes of convex and linear integer programming problems in variable dimension; and a complete complexity classification of high dimensional transportation problems, with practical applications to fundamental problems in privacy and confidential statistical data disclosure.
Sequential Vector Packing ⋆
"... Abstract. We introduce a novel variant of the well known ddimensional bin (or vector) packing problem. Given a sequence of nonnegative ddimensional vectors, the goal is to pack these into as few bins as possible of smallest possible size. In the classical problem the bin size vector is given and ..."
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Abstract. We introduce a novel variant of the well known ddimensional bin (or vector) packing problem. Given a sequence of nonnegative ddimensional vectors, the goal is to pack these into as few bins as possible of smallest possible size. In the classical problem the bin size vector is given and the sequence can be partitioned arbitrarily. We study a variation where the vectors have to be packed in the order in which they arrive and the bin size vector can be chosen once in the beginning. This setting gives rise to two combinatorial problems: One in which we want to minimize the number of used bins for a given total bin size and one in which we want to minimize the total bin size for a given number of bins. We prove that both problems are NPhard and propose an LP based bicriteria ( 1 ε, 1)approximation algorithm. We give a 2approximation
Convex Discrete Optimization
"... We develop an algorithmic theory of convex optimization over discrete sets. Using a combination of algebraic and geometric tools we are able to provide polynomial time algorithms for solving broad classes of convex combinatorial optimization problems and convex integer programming problems in variab ..."
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We develop an algorithmic theory of convex optimization over discrete sets. Using a combination of algebraic and geometric tools we are able to provide polynomial time algorithms for solving broad classes of convex combinatorial optimization problems and convex integer programming problems in variable dimension. We discuss some of the many applications of this theory including to quadratic programming, matroids, bin packing and cuttingstock problems, vector partitioning and clustering, multiway transportation problems, and privacy and confidential statistical data disclosure. Highlights of our work include a strongly polynomial time algorithm for convex and linear combinatorial optimization over any family presented by a membership oracle when the underlying polytope has few edgedirections; a new theory of sotermed nfold integer programming, yielding polynomial time solution of important and natural classes of convex and linear integer programming problems in variable dimension; and a complete complexity classification of high dimensional transportation problems, with practical applications to fundamental
Scheduling Dags under Uncertainty ∗
, 2008
"... This paper introduces a parallel scheduling problem where a directed acyclic graph modeling t tasks and their dependencies needs to be executed on n unreliable workers. Worker i executes task j correctly with probability pi,j. The goal is to find a regimen Σ, that dictates how workers get assigned t ..."
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This paper introduces a parallel scheduling problem where a directed acyclic graph modeling t tasks and their dependencies needs to be executed on n unreliable workers. Worker i executes task j correctly with probability pi,j. The goal is to find a regimen Σ, that dictates how workers get assigned to tasks (possibly in parallel and redundantly) throughout execution, so as to minimize the expected completion time. This fundamental parallel scheduling problem arises in grid computing and project management fields, and has several applications. We show a polynomial time algorithm for the problem restricted to the case when dag width is at most a constant and the number of workers is also at most a constant. These two restrictions may appear to be too severe. However, they are fundamentally required. Specifically, we demonstrate that the problem is NPhard with constant number of workers when dag width can grow, and is also NPhard with constant dag width when the number of workers can grow. When both dag width and the number of workers are unconstrained, then the problem is inapproximable within factor less than 5/4, unless P=NP.