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19
Minimizing Register Requirements of a Modulo Schedule via Optimum Stage Scheduling
 INTERNATIONAL JOURNAL OF PARALLEL PROGRAMMING
, 1996
"... Modulo scheduling is an efficient technique for exploiting instruction level parallelism in a variety of loops, resulting in high performance code but increased register requirements. We present an approach that schedules the loop operations for minimum register requirements, given a modulo reservat ..."
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Modulo scheduling is an efficient technique for exploiting instruction level parallelism in a variety of loops, resulting in high performance code but increased register requirements. We present an approach that schedules the loop operations for minimum register requirements, given a modulo reservation table. Our method determines optimal register requirements for machines with finite resources and for general dependence graphs. Measurements on a benchmark suite of 1327 loops from the Perfect Club, SPEC89, and the Livermore Fortran Kernels show that the register requirements decrease by 24.5% on average when applying the optimal stage scheduler to the MRTschedules of a registerinsensitive modulo scheduler.
Union of All the Minimum Cycle Bases of a Graph
, 1997
"... The perception of cyclic structures is a crucial step in the analysis of graphs. To describe the cycle vector space of a graph, a minimum cycle basis can be computed in polynomial time using an algorithm of [Horton, 1987]. But the set of cycles corresponding to a minimum basis is not always relev ..."
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Cited by 17 (0 self)
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The perception of cyclic structures is a crucial step in the analysis of graphs. To describe the cycle vector space of a graph, a minimum cycle basis can be computed in polynomial time using an algorithm of [Horton, 1987]. But the set of cycles corresponding to a minimum basis is not always relevant for analyzing the cyclic structure of a graph. This restriction is due to the fact that a minimum cycle basis is generally not unique for a given graph. Therefore, the smallest canonical set of cycles which describes the cyclic structure of a graph is the union of all the minimum cycle bases . This set of cycles is called the set of relevant cycles and denoted by CR . A relevant cycle can also be defined as a cycle which is not the sum of shorter cycles. A polynomial algorithm is presented that computes a compact representation of the potentially exponentialsized set CR in O(m 3 ) (where denotes the cyclomatic number). This compact representation consists of a polynomial nu...
Mathematical models and a constructive heuristic for finding minimum fundamental cycle bases
, 2003
"... Abstract: The problem of finding a fundamental cycle basis with minimum total cost in a graph arises in many application fields. In this paper we present some integer linear programming formulations and we compare their performances, in terms of instance size, CPU time required for the solution, and ..."
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Abstract: The problem of finding a fundamental cycle basis with minimum total cost in a graph arises in many application fields. In this paper we present some integer linear programming formulations and we compare their performances, in terms of instance size, CPU time required for the solution, and quality of the associated lower bound derived by solving the corresponding continuous relaxations. Since only very small instances can be solved to optimality with these formulations and very large instances occur in a number of applications, we present a new constructive heuristic and compare it with alternative heuristics.
Modulo Scheduling, Machine Representations, and RegisterSensitive Algorithms
, 1997
"... High performance compilers increasingly rely on accurate modeling of the machine resources to efficiently exploit the instruction level parallelism of an application. In this dissertation, we first propose a reduced machine description that results in significantly faster detection of resource con ..."
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High performance compilers increasingly rely on accurate modeling of the machine resources to efficiently exploit the instruction level parallelism of an application. In this dissertation, we first propose a reduced machine description that results in significantly faster detection of resource contentions while preserving the scheduling constraints present in the original machine description. This approach reduces a machine description in an automated, errorfree, and efficient fashion. Moreover, it fully supports the elaborate scheduling techniques that are used by highperformance compilers, such as scheduling an operation earlier than others that are already scheduled, unscheduling operations due to resource conflicts, and efficient handling of periodic resource requirements found in software pipelined schedules. Re...
DESIGN OF SURVIVABLE WDM NETWORK BASED ON PRECONFIGURED PROTECTION CYCLE By
, 2007
"... You may print or download ONE copy of this document for the purpose of your own research or study. The University does not authorize you to copy, communicate or otherwise make available electronically to any other person any copyright material contained on this site. You are reminded of the followi ..."
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You may print or download ONE copy of this document for the purpose of your own research or study. The University does not authorize you to copy, communicate or otherwise make available electronically to any other person any copyright material contained on this site. You are reminded of the following: Copyright owners are entitled to take legal action against persons who infringe their copyright. A reproduction of material that is protected by copyright may be a copyright infringement. A court may impose penalties and award damages in relation to offences and infringements relating to copyright material. Higher penalties may apply, and higher damages may be awarded, for offences and infringements involving the conversion of material into digital or electronic form.
Factoring Integers with LargePrime Variations of the Quadratic Sieve
, 1995
"... This article is concerned with the largeprime variations of the multipolynomial quadratic sieve factorization method: the PMPQS (one large prime) and the PPMPQS (two). We present the results of many factorization runs with the PMPQS and PPMPQS on SGI workstations and on a Cray C90 vector computer. ..."
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This article is concerned with the largeprime variations of the multipolynomial quadratic sieve factorization method: the PMPQS (one large prime) and the PPMPQS (two). We present the results of many factorization runs with the PMPQS and PPMPQS on SGI workstations and on a Cray C90 vector computer. Experiments show that for our Cray C90 implementations PPMPQS beats PMPQS for numbers of more than 80 digits, and that this crossover point goes down with the amount of available central memory. For PMPQS we give a formula to predict the total running time based on a short test run. The accuracy of the prediction is within 10% of the actual running time. For PPMPQS we do not have such a formula. Yet in order to provide measurements to help determining a good choice of the parameters in PPMPQS, we factored many numbers. In addition we give an experimental prediction formula for PPMPQS suitable if one wishes to factor many large numbers of about the same size. 1. INTRODUCTION
Model Counting for 2SAT Based on Graphs by Matrix Operators
"... Abstract—Counting the models of Boolean formulae is known to be intractable but pops up often in diverse areas. We focus in a restricted version of the problem. In particular, our results are based on matrix operators and Hadamard product for counting models of Boolean formulae consisting of chains ..."
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Abstract—Counting the models of Boolean formulae is known to be intractable but pops up often in diverse areas. We focus in a restricted version of the problem. In particular, our results are based on matrix operators and Hadamard product for counting models of Boolean formulae consisting of chains and embedded cycles. We obtain an efficient algorithm such that the input is a Boolean formula Σ in 2CNF and the output can be either a charged Boolean formula Σ ′ simpler than Σ or the number of models of Σ (the charge of a Boolean formula Σ is introduced as a vector in N 2, which contains information about the number of models of Σ). In the latter case, Σ belongs to a tractable class of Boolean formulae in 2CNF for #SAT that contains the classes 2µ2SAT and Acyclic2HORN.
Study of the implementation of BranchandCut as applied to Ising Spin Glasses
, 2007
"... Combinatorial Optimisation is a branch of Mathematics involved in finding the optimal (according to some criteria) combination among a finite set of possibilities. One such problem is finding the lowest energy state of the Ising Spin Glass, a model of disordered systems used in Statistical Physics. ..."
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Combinatorial Optimisation is a branch of Mathematics involved in finding the optimal (according to some criteria) combination among a finite set of possibilities. One such problem is finding the lowest energy state of the Ising Spin Glass, a model of disordered systems used in Statistical Physics. To solve the Ising Spin Glass exactly we can solve an integer linear programming problem. In a linear programming problem we want to find the real value of a set of N variables that maximise a given function subject to M linear inequalities in these variables. This can be solved by the Simplex and the DualSimplex algorithms. In an integer linear programming problem we have an additional constraint, that all the variables are integers: in this case we cannot use the simple Simplex/DualSimplex anymore but require an extension: the BranchandCut algorithm. We have implemented the BranchandCut algorithm to solve the maxcut problem in graph theory: the Ising Spin Glass problem can be converted into a maxcut problem in polynomial time. Coding the BranchandCut algorithm was in the end much more complicated than expected because it is itself made of many smaller problems that we
Declaration
, 2010
"... This dissertation may be made available for consultation within the University Library and may be photocopied or lent to other libraries for the purposes of consultation. Signed: GPU Integer Factorisation with the Quadratic Sieve ..."
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This dissertation may be made available for consultation within the University Library and may be photocopied or lent to other libraries for the purposes of consultation. Signed: GPU Integer Factorisation with the Quadratic Sieve