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Code Optimization by Integer Linear Programming [chapter]

Daniel Kästner, Marc Langenbach
1999 Lecture Notes in Computer Science  
By using integer linear programming (ILP), the deficiencies of the decoupling of different code generation phases can be removed, since it is possible to integrate instruction scheduling and register assignment  ...  Our experiments show, that approximations based on integer linear programming can provide a better solution quality than classical code generation algorithms in acceptable runtime for medium sized code  ...  Moreover, partitioning techniques have to be developed which allow also for larger code sequences to be optimized by integer linear programming.  ... 
doi:10.1007/978-3-540-49051-7_9 fatcat:hxpdfir4jvexpp3f276zewefqu

Solution of structural optimization problems by piecewise linearization

R. Lorentzen
1982 Quarterly of Applied Mathematics  
They can then be solved by the highly effective linear programming computer codes currently available. 1. Introduction.  ...  If the problem is convex, the linearization results in a linear programming problem without integer variables.  ...  If the problem is convex, the linearization results in a linear programming problem without integer variables.  ... 
doi:10.1090/qam/678207 fatcat:h5fe6kpnvfh55oddkguf34fj2u

Optimal vs. heuristic integrated code generation for clustered VLIW architectures

Mattias V. Eriksson, Oskar Skoog, Christoph W. Kessler
2008 Proceedings of the 11th international workshop on Software & compilers for embedded systems - SCOPES '08  
has two methods for optimal integrated code generation (CG) ◮ Dynamic programmingInteger Linear Programming ◮ We extend OPTIMIST by: ◮ Generalizing ILP to clustered architectures ◮ Adding  ...  Code Generation Optimal Method -Integer Linear Programming Heuristic Method -Genetic Algorithm Evaluation Experimental Results Conclusions Our Contributions Integrated Code Generation ◮ The  ...  ◮ ILP finds optimal solutions for moderately large problems. And the rest of the problems may be solved by the GA. ◮ When optimal solution is known, GA finds it 85% of the time  ... 
doi:10.1145/1361096.1361099 dblp:conf/scopes/ErikssonSK08 fatcat:iiscxkcqgvgvznp5gkqbjrg2fy

An Improved Decomposition Technique for Solving Integer Linear Programming Problems

M. A., M. S.
2018 International Journal of Computer Applications  
Decomposition technique is one of the most frequently used technique for solving Linear Programming Problems (LPPs) as well as Integer Linear Programming Problems (ILPPs).  ...  This paper proposes a new technique for solving a ILLP manually and develops a computer code using a Mathematical Programming Language (AMPL).  ...  The Integer Linear Programming Problem (ILPP) is one of the latest LP problems which refer to the class of combinatorial constrained optimization problems with integer variables, where the objective function  ... 
doi:10.5120/ijca2018918023 fatcat:cxwzqrg2zbe6zpbcgry7hvtpbq

Recent developments and future directions in mathematical programming

E. L. Johnson, G. L. Nemhauser
1992 IBM Systems Journal  
greater function of optimization codes.  ...  programming using strong linear programming formulations, and a renewed interest in decomposition.  ...  The important fact about network flow problems is that they can be solved by specialized simplex codes much faster than by using a general linear programming code.  ... 
doi:10.1147/sj.311.0079 fatcat:wanug5bsafdblohniet3jj4yp4

An improved branch and bound algorithm for mixed integer nonlinear programs

Brian Borchers, John E. Mitchell
1994 Computers & Operations Research  
Scope and Purpose-Mixed integer programming problems are optimization problems in which some or all of the variables are allowed to take on only integer values.  ...  The code uses Lagrangian duality to obtain lower bounds. The code also uses early branching to avoid solving some subproblems to optimality.  ...  Acknowledgement-This research was partially supported by ONR Grant number NOOO14-90-J-1714.  ... 
doi:10.1016/0305-0548(94)90024-8 fatcat:oluetwb3uncxvla4nkmbmsktra

Page 330 of Mathematical Reviews Vol. 57, Issue 1 [page]

1979 Mathematical Reviews  
An (n, k) binary linear code is a k-dimensional subspace of the vector space of n-tuples with components from GF(2). (It there- fore has 2* code words.)  ...  Any relaxation of the constraints in an integer program mre 7 Ax3b, x integer} leads to a problem of the form min{c’x| A,x<b,, x integer}, where A,, b, are the parts of A and b defined by a set of indices  ... 

Fast linear programming through transprecision computing on small and sparse data

Tobias Grosser, Theodoros Theodoridis, Maximilian Falkenstein, Arjun Pitchanathan, Michael Kruse, Manuel Rigger, Zhendong Su, Torsten Hoefler
2020 Proceedings of the ACM on Programming Languages (PACMPL)  
A plethora of program analysis and optimization techniques rely on linear programming at their heart. However, such techniques are often considered too slow for production use.  ...  As a result, compilers do not benefit from decades of research on optimizing large-scale linear programming. We design a simplex solver targeted at compilers.  ...  We obtain detailed statistics by tracing and analyzing linear programs in three key areas: analytical modeling, polyhedral loop optimization, and accelerator code generation.  ... 
doi:10.1145/3428263 fatcat:4dtoj7cq35es3n4ophpnig44ou

Page 291 of Geographical Analysis Vol. 8, Issue 3 [page]

1976 Geographical Analysis  
This special structure can be solved with suitable special computer codes two orders of magnitude faster than with general-purpose linear programming codes.  ...  An additional property of an exact optimal solution to such a convex programming problem is that a large fraction of the optimal t,, must be noninteger.  ... 

Network Coding for Multiple Unicasts: An Approach based on Linear Optimization

Danail Traskov, Niranjan Ratnakar, Desmond Lun, Ralf Koetter, Muriel Medard
2006 2006 IEEE International Symposium on Information Theory  
One consists of a linear program and the other of an integer program with fewer variables and constraints. We discuss the performance of the proposed techniques as well as their complexity.  ...  In this paper we consider the application of network coding to a multiple unicast setup. We present two suboptimal, yet practical code construction techniques.  ...  Since both the linear and the integer program model the same problem, the linear program in this case would have given equivalent results. 4 By optimal routing we mean the optimal solution of the associated  ... 
doi:10.1109/isit.2006.261656 dblp:conf/isit/TraskovRLKM06 fatcat:swfjn3isujgfnbxlernw4xio2i

A comparative study of SQP-type algorithms for nonlinear and nonconvex mixed-integer optimization

Oliver Exler, Thomas Lehmann, Klaus Schittkowski
2012 Mathematical Programming Computation  
We present numerical results of a comparative study of codes for nonlinear and nonconvex mixed-integer optimization.  ...  The mixed-integer quadratic programming subproblems are solved by a branch-and-cut algorithm.  ...  Convergence towards the global optimal solution of a convex program is guaranteed by considering a gradually improving mixed-integer linear relaxation of the original mixed-integer nonlinear program.  ... 
doi:10.1007/s12532-012-0045-0 fatcat:og2s7nejq5hzrkfez2ob4mtfbi

Duality Codes and the Integrality Gap Bound for Index Coding

Hao Yu, Michael J. Neely
2014 IEEE Transactions on Information Theory  
Thus, the information theoretic optimum is bounded by the integrality gap between the integer program and its linear relaxation.  ...  Conversely, its linear programming relaxation is shown to provide an upper bound that is achievable by a simple form of vector linear coding.  ...  Hence, the performance gap between the optimal index code and the optimal vector cyclic code is ultimately bounded by the integrality gap between integer program (P1) and its LP relaxation (P1 ).  ... 
doi:10.1109/tit.2014.2354044 fatcat:plhfz5ptqfeojmujtl7dmfnpy4

Duality codes and the integrality gap bound for index coding

Hao Yu, Michael J. Neely
2013 2013 51st Annual Allerton Conference on Communication, Control, and Computing (Allerton)  
Thus, the information theoretic optimum is bounded by the integrality gap between the integer program and its linear relaxation.  ...  Conversely, its linear programming relaxation is shown to provide an upper bound that is achievable by a simple form of vector linear coding.  ...  Hence, the performance gap between the optimal index code and the optimal vector cyclic code is ultimately bounded by the integrality gap between integer program (P1) and its LP relaxation (P1 ).  ... 
doi:10.1109/allerton.2013.6736712 dblp:conf/allerton/YuN13 fatcat:hxnkeded4fabxjpfgqwqafal2i

Maximum independent set (stable set) problem: A mathematical programming model with valid inequalities and computational testing [article]

Prabhu Manyem
2022 arXiv   pre-print
In each of these instances, the Linear Relaxation returned an optimal solution with (i) every variable having an integer value, and (ii) the optimal solution value of the Linear Relaxation was the same  ...  The basic mathematical programming model that captures this problem is an Integer Program (I.P.) with zero-one variables and only the edge inequalities.  ...  .) = Optimal value of the original Integer Program in Problem 1.  ... 
arXiv:2206.12531v5 fatcat:oqa7k3emqjejdebgomumu7re6q

Page 7701 of Mathematical Reviews Vol. , Issue 2002J [page]

2002 Mathematical Reviews  
The obtained approximation is reduced to a nonlinear programming problem which can be solved by means of standard techniques of linear/quadratic programming.”  ...  We apply this result to solve linear integer programming problems with m ¢ n inequalities.” 2002j:90046 90C10 90C57 Valerio de Carvalho, J. M.  ... 
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