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

2022
*
arXiv
*
pre-print

We design a fixed parameter

arXiv:1907.06688v5
fatcat:vnbpi6qmdzdqrb72cq2gcuvohm
*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. ...##
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Matrices of Optimal Tree-Depth and Row-Invariant Parameterized Algorithm for Integer Programming

2020
*
International Colloquium on Automata, Languages and Programming
*

Finally, we use these results to obtain a fixed parameter

doi:10.4230/lipics.icalp.2020.26
dblp:conf/icalp/ChanCKKP20
fatcat:mq36yhlxzzgkpap2xq7jijqix4
*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 . ...##
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Characterization of matrices with bounded Graver bases and depth parameters and applications to integer programming
[article]

2022
*
arXiv
*
pre-print

In particular,

arXiv:2202.05299v3
fatcat:u77lszicbzfjnlhs3tj7tidayy
*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 ...##
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Putting Polyhedral Loop Transformations to Work
[chapter]

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 ...

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

2004
*
Lecture Notes in Computer Science
*

Our framework is well suited

doi:10.1007/978-3-540-27866-5_38
fatcat:tegxfpz7obdmtiaslfw5wlfhbq
*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. ...##
###
d-COS-R is FPT via Interval Deletion
[article]

2013
*
arXiv
*
pre-print

In this work, we describe a recursive

arXiv:1303.1643v1
fatcat:bar5qkmmrzburaeliuvzqxlrqm
*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. ...##
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Problem-specific Parameterized Quantum Circuits of the VQE Algorithm for Optimization Problems
[article]

2020
*
arXiv
*
pre-print

Creating sophisticated PQCs is important from the perspective

arXiv:2006.05643v2
fatcat:kmmpjaf6arcyfc7d6k4dk3iyqi
*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. ...##
###
Fully polynomial-time parameterized computations for graphs and matrices of low treewidth
[article]

2015
*
arXiv
*
pre-print

Namely, the

arXiv:1511.01379v1
fatcat:3icfmhm2b5hcpg4l2mtxlkv5fm
*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. ...##
###
The Complexity Landscape of Decompositional Parameters for ILP: Programs with Few Global Variables and Constraints

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). ...

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

2016
*
arXiv
*
pre-print

They also show that REMBO achieves state-

arXiv:1301.1942v2
fatcat:aa4lugkjd5b45hgje26bkzddxe
*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. ...##
###
Semi-Automatic Composition of Loop Transformations for Deep Parallelism and Memory Hierarchies

2006
*
International journal of parallel programming
*

Modern compilers are responsible

doi:10.1007/s10766-006-0012-3
fatcat:czrbuhejuzht5htht4idcisewe
*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. ...##
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An Algorithmic Theory of Integer Programming
[article]

2022
*
arXiv
*
pre-print

In particular, we develop near-linear time

arXiv:1904.01361v3
fatcat:5jihvj5fvfbgthqid5o7ulcsrm
*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). ...##
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Digital VLSI Implementation of Piecewise-Affine Controllers Based on Lattice Approach

2015
*
IEEE Transactions on Control Systems Technology
*

The architecture is

doi:10.1109/tcst.2014.2345094
fatcat:4uj4nwvctnb4xjxgsngkeu7y4a
*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. ...##
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Serial and parallel kernelization of Multiple Hitting Set parameterized by the Dilworth number, implemented on the GPU
[article]

2021
*
arXiv
*
pre-print

Generalizing a well-known data reduction

arXiv:2109.06042v1
fatcat:o6phw72qv5fvdi7d2zihyeftpe
*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. ...##
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Lattice Enumeration Using Extreme Pruning
[chapter]

2010
*
Lecture Notes in Computer Science
*

Lattice enumeration

doi:10.1007/978-3-642-13190-5_13
fatcat:qha3mzjtlrec7all4k65jds4xe
*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] ...
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