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Code Optimization by Integer Linear Programming
[chapter]

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*. ...

##
###
Solution of structural optimization problems by piecewise linearization

1982
*
Quarterly of Applied Mathematics
*

They can then be solved

doi:10.1090/qam/678207
fatcat:h5fe6kpnvfh55oddkguf34fj2u
*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. ...##
###
Optimal vs. heuristic integrated code generation for clustered VLIW architectures

2008
*
Proceedings of the 11th international workshop on Software & compilers for embedded systems - SCOPES '08
*

has
two methods for

doi:10.1145/1361096.1361099
dblp:conf/scopes/ErikssonSK08
fatcat:iiscxkcqgvgvznp5gkqbjrg2fy
*optimal*integrated*code*generation (CG) ◮ Dynamic*programming*◮*Integer**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 ...##
###
An Improved Decomposition Technique for Solving Integer Linear Programming Problems

2018
*
International Journal of Computer Applications
*

Decomposition technique is one of the most frequently used technique for solving

doi:10.5120/ijca2018918023
fatcat:cxwzqrg2zbe6zpbcgry7hvtpbq
*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 ...##
###
Recent developments and future directions in mathematical programming

1992
*
IBM Systems Journal
*

greater function of

doi:10.1147/sj.311.0079
fatcat:wanug5bsafdblohniet3jj4yp4
*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*. ...##
###
An improved branch and bound algorithm for mixed integer nonlinear programs

1994
*
Computers & Operations Research
*

Scope and Purpose-Mixed

doi:10.1016/0305-0548(94)90024-8
fatcat:oluetwb3uncxvla4nkmbmsktra
*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. ...##
###
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

2020
*
Proceedings of the ACM on Programming Languages (PACMPL)
*

A plethora of

doi:10.1145/3428263
fatcat:4dtoj7cq35es3n4ophpnig44ou
*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. ...##
###
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

2006
*
2006 IEEE International Symposium on Information Theory
*

One consists of a

doi:10.1109/isit.2006.261656
dblp:conf/isit/TraskovRLKM06
fatcat:swfjn3isujgfnbxlernw4xio2i
*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 ...##
###
A comparative study of SQP-type algorithms for nonlinear and nonconvex mixed-integer optimization

2012
*
Mathematical Programming Computation
*

We present numerical results of a comparative study of

doi:10.1007/s12532-012-0045-0
fatcat:og2s7nejq5hzrkfez2ob4mtfbi
*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*. ...##
###
Duality Codes and the Integrality Gap Bound for Index Coding

2014
*
IEEE Transactions on Information Theory
*

Thus, the information theoretic optimum is bounded

doi:10.1109/tit.2014.2354044
fatcat:plhfz5ptqfeojmujtl7dmfnpy4
*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 ). ...##
###
Duality codes and the integrality gap bound for index coding

2013
*
2013 51st Annual Allerton Conference on Communication, Control, and Computing (Allerton)
*

Thus, the information theoretic optimum is bounded

doi:10.1109/allerton.2013.6736712
dblp:conf/allerton/YuN13
fatcat:hxnkeded4fabxjpfgqwqafal2i
*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 ). ...##
###
Maximum independent set (stable set) problem: A mathematical programming model with valid inequalities and computational testing
[article]

2022
*
arXiv
*
pre-print

In each of these instances, the

arXiv:2206.12531v5
fatcat:oqa7k3emqjejdebgomumu7re6q
*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. ...##
###
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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