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Matrices of optimal tree-depth and a row-invariant parameterized algorithm for integer programming [article]

Timothy F. N. Chan, Jacob W. Cooper, Martin Koutecky, Daniel Kral, Kristyna Pekarkova
2022 arXiv   pre-print
We design a fixed parameter algorithm for computing branch-depth of matroids represented over a finite field and a fixed parameter algorithm for computing a row-equivalent matrix with minimum dual tree-depth  ...  A long line of research on fixed parameter tractability of integer programming culminated with showing that integer programs with n variables and a constraint matrix with dual tree-depth d and largest  ...  Acknowledgement The authors would like to thank the anonymous reviewers for their comments, which significantly improved the presentation of the paper and its results.  ... 
arXiv:1907.06688v5 fatcat:vnbpi6qmdzdqrb72cq2gcuvohm

Matrices of Optimal Tree-Depth and Row-Invariant Parameterized Algorithm for Integer Programming

Timothy F. N. Chan, Jacob W. Cooper, Martin Koutecký, Daniel Král', Kristýna Pekárková, Emanuela Merelli, Artur Czumaj, Anuj Dawar
2020 International Colloquium on Automata, Languages and Programming  
Finally, we use these results to obtain a fixed parameter algorithm for integer programming parameterized by the branch-depth of the input constraint matrix and the entry complexity.  ...  We also design a fixed parameter algorithm parameterized by an integer d and the entry complexity of an input matrix that either outputs a matrix with the smallest dual tree-depth that is row-equivalent  ...  We now demonstrate the drawback of the parameterization of integer programs by tree-depth that we have mentioned earlier. Consider the following matrices A and A .  ... 
doi:10.4230/lipics.icalp.2020.26 dblp:conf/icalp/ChanCKKP20 fatcat:mq36yhlxzzgkpap2xq7jijqix4

Characterization of matrices with bounded Graver bases and depth parameters and applications to integer programming [article]

Marcin Brianski, Martin Koutecky, Daniel Kral, Kristyna Pekarkova, Felix Schroder
2022 arXiv   pre-print
In particular, integer programming is fixed parameter tractable when parameterized by the primal tree-depth and the entry complexity of A, and when parameterized by the dual tree-depth and the entry complexity  ...  Our results yield parameterized algorithms for integer programming when parameterized by the ℓ_1-norm of the Graver basis of the constraint matrix, when parameterized by the ℓ_1-norm of the circuits of  ...  Acknowledgements All five authors would like to thank the Schloss Dagstuhl--Leibniz Center for Informatics for hospitality during the workshop "Sparsity in Algorithms, Combinatorics and Logic" in September  ... 
arXiv:2202.05299v3 fatcat:u77lszicbzfjnlhs3tj7tidayy

Putting Polyhedral Loop Transformations to Work [chapter]

Cédric Bastoul, Albert Cohen, Sylvain Girbal, Saurabh Sharma, Olivier Temam
2004 Lecture Notes in Computer Science  
For that purpose, we need a generic way to express program transformations and compositions of transformations.  ...  We seek to extend the scope and efficiency of iterative compilation techniques by searching not only for program transformation parameters but for the most appropriate transformations themselves.  ...  It is intended as a formal tool for semi-automatic optimization, where program transformations -with the associated static analyses for semantic-preservation -are separated from the optimization or parallelization  ... 
doi:10.1007/978-3-540-24644-2_14 fatcat:4fs64up7dvdxvo4ylkie7lpyvm

A Polyhedral Approach to Ease the Composition of Program Transformations [chapter]

Albert Cohen, Sylvain Girbal, Olivier Temam
2004 Lecture Notes in Computer Science  
Our framework is well suited for iterative optimization techniques searching not only for the appropriate parameters of a given transformation, but for the program transformations themselves, and especially  ...  for compositions of program transformations.  ...  We are very thankful to Cedric Bastoul and Saurabh Sharma, whose algorithms, tools and support have been critical for the design and implementation of our framework.  ... 
doi:10.1007/978-3-540-27866-5_38 fatcat:tegxfpz7obdmtiaslfw5wlfhbq

d-COS-R is FPT via Interval Deletion [article]

N.S. Narayanaswamy, R. Subashini
2013 arXiv   pre-print
In this work, we describe a recursive depth-bounded search tree algorithm in which the problems at the leaf-level are solved as instances of Interval Deletion.  ...  We consider the parameterized complexity of this problem with respect to the number d of rows to be deleted as the parameter.  ...  Here, the inputs to the algorithm are the half adjacency matrix M of G and the parameter d.  ... 
arXiv:1303.1643v1 fatcat:bar5qkmmrzburaeliuvzqxlrqm

Problem-specific Parameterized Quantum Circuits of the VQE Algorithm for Optimization Problems [article]

Atsushi Matsuo, Yudai Suzuki, Shigeru Yamashita
2020 arXiv   pre-print
Creating sophisticated PQCs is important from the perspective of the convergence speed. Thus, we propose problem-specific PQCs of the VQE algorithm for optimization problems.  ...  The VQE algorithm requires a quantum circuit with parameters, called a parameterized quantum circuit (PQC), to prepare a quantum state, and the quantum state is used to calculate the expectation value  ...  Although the VQE algorithm is being studied intensively and PQCs of the VQE algorithm is important, there are a few researches considering PQCs of the VQE algorithm for the optimization problems.  ... 
arXiv:2006.05643v2 fatcat:kmmpjaf6arcyfc7d6k4dk3iyqi

Fully polynomial-time parameterized computations for graphs and matrices of low treewidth [article]

Fedor V. Fomin, Daniel Lokshtanov, Michał Pilipczuk, Saket Saurabh, Marcin Wrochna
2015 arXiv   pre-print
Namely, the algorithm, when given a graph G and integer k, runs in time O(k^7· n n) and either correctly reports that the treewidth of G is larger than k, or constructs a tree decomposition of G of width  ...  Our results include: -- an algorithm for computing the determinant and the rank of an n× n matrix using O(k^3· n) time and arithmetic operations; -- an algorithm for solving a system of linear equations  ...  The goal of this paper is to provide solid algorithmic foundations for the further study of fully polynomial parameterized algorithms on graphs and matrices of low treewidth.  ... 
arXiv:1511.01379v1 fatcat:3icfmhm2b5hcpg4l2mtxlkv5fm

The Complexity Landscape of Decompositional Parameters for ILP: Programs with Few Global Variables and Constraints

Pavel Dvořák, Eduard Eiben, Robert Ganian, Dušan Knop, Sebastian Ordyniak
2021 Artificial Intelligence  
Integer Linear Programming (ILP) has a broad range of applications in various areas of artificial intelligence.  ...  Second, we exploit these backdoors to develop several new parameterized algorithms for ILP; the performance of these algorithms will naturally scale based on the number of global variables or constraints  ...  Acknowledgments Robert Ganian acknowledges support by the Austrian Science Fund (FWF, projects P31336 and Y1329).  ... 
doi:10.1016/j.artint.2021.103561 fatcat:jhb3n6e3qbapjppl73lxsnafoe

Bayesian Optimization in a Billion Dimensions via Random Embeddings [article]

Ziyu Wang, Frank Hutter, Masrour Zoghi, David Matheson, Nando de Freitas
2016 arXiv   pre-print
They also show that REMBO achieves state-of-the-art performance in optimizing the 47 discrete parameters of a popular mixed integer linear programming solver.  ...  The resulting Random EMbedding Bayesian Optimization (REMBO) algorithm is very simple, has important invariance properties, and applies to domains with both categorical and continuous variables.  ...  Acknowledgements We thank Christof Schötz for proofreading a draft of this article.  ... 
arXiv:1301.1942v2 fatcat:aa4lugkjd5b45hgje26bkzddxe

Semi-Automatic Composition of Loop Transformations for Deep Parallelism and Memory Hierarchies

Sylvain Girbal, Nicolas Vasilache, Cédric Bastoul, Albert Cohen, David Parello, Marc Sigler, Olivier Temam
2006 International journal of parallel programming  
Modern compilers are responsible for translating the idealistic operational semantics of the source program into a form that makes efficient use of a highly complex heterogeneous machine.  ...  We address this challenge by working on the program representation itself, using a semi-automatic optimization approach to demonstrate that current compilers offen suffer from unnecessary constraints and  ...  Rice University, Greg Lindahl and Fred Chow from PathScale, and the UPC team at the University of California Berkeley.  ... 
doi:10.1007/s10766-006-0012-3 fatcat:czrbuhejuzht5htht4idcisewe

An Algorithmic Theory of Integer Programming [article]

Friedrich Eisenbrand, Christoph Hunkenschröder, Kim-Manuel Klein, Martin Koutecký, Asaf Levin, Shmuel Onn
2022 arXiv   pre-print
In particular, we develop near-linear time algorithms for n-fold, tree-fold, and 2-stage stochastic integer programs. We also discuss some of the many applications of these classes.  ...  In particular, integer programming is fixed-parameter tractable parameterized by a and d, and is solvable in polynomial time for every fixed a and d.  ...  the complexity of integer programming (Nr. 163071).  ... 
arXiv:1904.01361v3 fatcat:5jihvj5fvfbgthqid5o7ulcsrm

Digital VLSI Implementation of Piecewise-Affine Controllers Based on Lattice Approach

Macarena Cristina Martinez-Rodriguez, Piedad Brox, Iluminada Baturone
2015 IEEE Transactions on Control Systems Technology  
The architecture is parameterized in terms of number of inputs, outputs, signal resolution, and features of the controller to be generated.  ...  The design flows for Field Programmable Gate Arrays (FPGAs) and Application Specific Integrated Circuits (ASICs) are detailed.  ...  Martínez-Rodríguez is supported by FPI fellowship program for Ph.D. Students from Spanish Government. P. Brox is supported by 'V Plan Propio de Investigación' from the University of Seville.  ... 
doi:10.1109/tcst.2014.2345094 fatcat:4uj4nwvctnb4xjxgsngkeu7y4a

Serial and parallel kernelization of Multiple Hitting Set parameterized by the Dilworth number, implemented on the GPU [article]

René van Bevern and Artem M. Kirilin and Daniel A. Skachkov and Pavel V. Smirnov and Oxana Yu. Tsidulko
2021 arXiv   pre-print
Generalizing a well-known data reduction algorithm due to Weihe, we show a problem kernel for Multiple Hitting Set parameterized by the Dilworth number, a graph parameter introduced by Foldes and Hammer  ...  in 1978 yet seemingly so far unexplored in the context of parameterized complexity theory.  ...  The lower bound L j can be obtained, for example, via an integer linear programming relaxation.  ... 
arXiv:2109.06042v1 fatcat:o6phw72qv5fvdi7d2zihyeftpe

Lattice Enumeration Using Extreme Pruning [chapter]

Nicolas Gama, Phong Q. Nguyen, Oded Regev
2010 Lecture Notes in Computer Science  
Lattice enumeration algorithms are the most basic algorithms for solving hard lattice problems such as the shortest vector problem and the closest vector problem, and are often used in public-key cryptanalysis  ...  Here we revisit these fundamental algorithms and show that surprising exponential speedups can be achieved both in theory and in practice by using a new technique, which we call extreme pruning.  ...  Algorithms for these problems can be used to solve a wide range of problems, such as integer programming [16] , factoring polynomials with rational coefficients [17] , integer relation finding [15]  ... 
doi:10.1007/978-3-642-13190-5_13 fatcat:qha3mzjtlrec7all4k65jds4xe
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