Results 11  20
of
1,195
Parametric Integer Programming
 RAIRO Recherche Op'erationnelle
, 1988
"... When analysing computer programs (especially numerical programs in which arrays are used extensively), one is often confronted with integer programming problems. These problems have three peculiarities: ffl feasible points are ranked according to lexicographic order rather than the usual linear ec ..."
Abstract

Cited by 164 (19 self)
 Add to MetaCart
When analysing computer programs (especially numerical programs in which arrays are used extensively), one is often confronted with integer programming problems. These problems have three peculiarities: ffl feasible points are ranked according to lexicographic order rather than the usual linear economic function; ffl the feasible set depends on integer parameters; ffl one is interested only in exact solutions. The difficulty is somewhat alleviated by the fact that problems sizes are usually quite small. In this paper we show that: ffl the classical simplex algorithm has no difficulty in handling lexicographic ordering; ffl the algorithm may be executed in symbolic mode, thus giving the solution of continuous parametric problems; ffl the method may be extended to problems in integers. We prove that the resulting algorithm always terminate and give an estimate of its complexity. R'esum'e L'analyse s'emantique des programmes (sp'ecialement des programmes num'eriques utilisant de...
Reverse Search for Enumeration
 Discrete Applied Mathematics
, 1993
"... The reverse search technique has been recently introduced by the authors for efficient enumeration of vertices of polyhedra and arrangements. In this paper, we develop this idea in a general framework and show its broader applications to various problems in operations research, combinatorics, and ..."
Abstract

Cited by 153 (25 self)
 Add to MetaCart
The reverse search technique has been recently introduced by the authors for efficient enumeration of vertices of polyhedra and arrangements. In this paper, we develop this idea in a general framework and show its broader applications to various problems in operations research, combinatorics, and geometry. In particular, we propose new algorithms for listing (i) all triangulations of a set of n points in the plane, (ii) all cells in a hyperplane arrangement in R d , (iii) all spanning trees of a graph, (iv) all Euclidean (noncrossing) trees spanning a set of n points in the plane, (v) all connected induced subgraphs of a graph, and (vi) all topological orderings of an acyclic graph. Finally we propose a new algorithm for the 01 integer programming problem which can be considered as an alternative to the branchandbound algorithm. 1 Introduction The listing of all objects that satisfy a specified property is a fundamental problem in combinatorics, computational geometr...
Practical Dependence Testing
, 1991
"... Precise and efficient dependence tests are essential to the effectiveness of a parallelizing compiler. This paper proposes a dependence testing scheme based on classifying pairs of subscripted variable references. Exact yet fast dependence tests are presented for certain classes of array references, ..."
Abstract

Cited by 138 (16 self)
 Add to MetaCart
Precise and efficient dependence tests are essential to the effectiveness of a parallelizing compiler. This paper proposes a dependence testing scheme based on classifying pairs of subscripted variable references. Exact yet fast dependence tests are presented for certain classes of array references, as well as empirical results showing that these references dominate scientific Fortran codes. These dependence tests are being implemented at Rice University in both PFC, a parallelizing compiler, and ParaScope, a parallel programming environment.
Probabilistic Logic Programming
, 1992
"... Of all scientific investigations into reasoning with uncertainty and chance, probability theory is perhaps the best understood paradigm. Nevertheless, all studies conducted thus far into the semantics of quantitative logic programming (cf. van Emden [51], Fitting [18, 19, 20], Blair and Subrahmanian ..."
Abstract

Cited by 131 (7 self)
 Add to MetaCart
Of all scientific investigations into reasoning with uncertainty and chance, probability theory is perhaps the best understood paradigm. Nevertheless, all studies conducted thus far into the semantics of quantitative logic programming (cf. van Emden [51], Fitting [18, 19, 20], Blair and Subrahmanian [5, 6, 49, 50], Kifer et al [29, 30, 31]) have restricted themselves to nonprobabilistic semantical characterizations. In this paper, we take a few steps towards rectifying this situation. We define a logic programming language that is syntactically similar to the annotated logics of [5, 6], but in which the truth values are interpreted probabilistically. A probabilistic model theory and fixpoint theory is developed for such programs. This probabilistic model theory satisfies the requirements proposed by Fenstad [16] for a function to be called probabilistic. The logical treatment of probabilities is complicated by two facts: first, that the connectives cannot be interpreted truth function...
A Survey of Computational Complexity Results in Systems and Control
, 2000
"... The purpose of this paper is twofold: (a) to provide a tutorial introduction to some key concepts from the theory of computational complexity, highlighting their relevance to systems and control theory, and (b) to survey the relatively recent research activity lying at the interface between these fi ..."
Abstract

Cited by 116 (21 self)
 Add to MetaCart
The purpose of this paper is twofold: (a) to provide a tutorial introduction to some key concepts from the theory of computational complexity, highlighting their relevance to systems and control theory, and (b) to survey the relatively recent research activity lying at the interface between these fields. We begin with a brief introduction to models of computation, the concepts of undecidability, polynomial time algorithms, NPcompleteness, and the implications of intractability results. We then survey a number of problems that arise in systems and control theory, some of them classical, some of them related to current research. We discuss them from the point of view of computational complexity and also point out many open problems. In particular, we consider problems related to stability or stabilizability of linear systems with parametric uncertainty, robust control, timevarying linear systems, nonlinear and hybrid systems, and stochastic optimal control.
Using linear programming to decode binary linear codes
 IEEE TRANS. INFORM. THEORY
, 2005
"... A new method is given for performing approximate maximumlikelihood (ML) decoding of an arbitrary binary linear code based on observations received from any discrete memoryless symmetric channel. The decoding algorithm is based on a linear programming (LP) relaxation that is defined by a factor grap ..."
Abstract

Cited by 113 (11 self)
 Add to MetaCart
A new method is given for performing approximate maximumlikelihood (ML) decoding of an arbitrary binary linear code based on observations received from any discrete memoryless symmetric channel. The decoding algorithm is based on a linear programming (LP) relaxation that is defined by a factor graph or paritycheck representation of the code. The resulting “LP decoder” generalizes our previous work on turbolike codes. A precise combinatorial characterization of when the LP decoder succeeds is provided, based on pseudocodewords associated with the factor graph. Our definition of a pseudocodeword unifies other such notions known for iterative algorithms, including “stopping sets, ” “irreducible closed walks, ” “trellis cycles, ” “deviation sets, ” and “graph covers.” The fractional distance ��— ™ of a code is introduced, which is a lower bound on the classical distance. It is shown that the efficient LP decoder will correct up to ��— ™ P I errors and that there are codes with ��— ™ a @ I A. An efficient algorithm to compute the fractional distance is presented. Experimental evidence shows a similar performance on lowdensity paritycheck (LDPC) codes between LP decoding and the minsum and sumproduct algorithms. Methods for tightening the LP relaxation to improve performance are also provided.
Code generation in the polyhedral model is easier than you think
 In IEEE Intl. Conf. on Parallel Architectures and Compilation Techniques (PACT’04
, 2004
"... Many advances in automatic parallelization and optimization have been achieved through the polyhedral model. It has been extensively shown that this computational model provides convenient abstractions to reason about and apply program transformations. Nevertheless, the complexity of code generation ..."
Abstract

Cited by 109 (16 self)
 Add to MetaCart
Many advances in automatic parallelization and optimization have been achieved through the polyhedral model. It has been extensively shown that this computational model provides convenient abstractions to reason about and apply program transformations. Nevertheless, the complexity of code generation has long been a deterrent for using polyhedral representation in optimizing compilers. First, code generators have a hard time coping with generated code size and control overhead that may spoil theoretical benefits achieved by the transformations. Second, this step is usually time consuming, hampering the integration of the polyhedral framework in production compilers or feedbackdirected, iterative optimization schemes. Moreover, current code generation algorithms only cover a restrictive set of possible transformation functions. This paper discusses a general transformation framework able to deal with nonunimodular, noninvertible, nonintegral or even nonuniform functions. It presents several improvements to a stateoftheart code generation algorithm. Two directions are explored: generated code size and code generator efficiency. Experimental evidence proves the ability of the improved method to handle reallife problems. 1.
A Library for Doing Polyhedral Operations
, 1993
"... Polyhedra are geometric representations of linear systems of equations and inequalities. Since polyhedra are used to represent the iteration domains of nested loop programs, procedures for operating on polyhedra are useful for doing loop transformations and other program restructuring transformatio ..."
Abstract

Cited by 107 (13 self)
 Add to MetaCart
Polyhedra are geometric representations of linear systems of equations and inequalities. Since polyhedra are used to represent the iteration domains of nested loop programs, procedures for operating on polyhedra are useful for doing loop transformations and other program restructuring transformations which are needed in parallelizing compilers. Thus a need for a library of polyhedral operations has recently been recognized in the parallelizing compiler community. Polyhedra are also used in the definition of domains of variables in systems of affine recurrence equations (SARE). Alpha is a language which is based on the SARE formalism in which all variables are declared over finite unions of polyhedra. This report describes a library of polyhedral functions which was developed to support the Alpha language environment, and which is general enough to satisfy the needs of researchers doing parallelizing compilers. This report describes the data structures used to represent domains, gives...
Automatic Program Parallelization
, 1993
"... This paper presents an overview of automatic program parallelization techniques. It covers dependence analysis techniques, followed by a discussion of program transformations, including straightline code parallelization, do loop transformations, and parallelization of recursive routines. The last s ..."
Abstract

Cited by 105 (8 self)
 Add to MetaCart
This paper presents an overview of automatic program parallelization techniques. It covers dependence analysis techniques, followed by a discussion of program transformations, including straightline code parallelization, do loop transformations, and parallelization of recursive routines. The last section of the paper surveys several experimental studies on the effectiveness of parallelizing compilers.