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Convex hulls of superincreasing knapsacks and lexicographic orderings

2016
*
Discrete Applied Mathematics
*

We also establish a distributive property by proving that the

doi:10.1016/j.dam.2015.08.010
fatcat:lzpvcljrc5bjfgy7pn7fjzbwjm
*convex**hull**of*<-*and*>-type*superincreasing**knapsacks*can be obtained by intersecting the*convex**hulls**of*<-*and*>-sets taken individually ... The elements*of*this*superincreasing**knapsack*are exactly those vectors that are*lexicographically*smaller than the greedy solution to optimizing over this*knapsack*. ... In Section 4, we prove that the*convex**hull**of*intersection*of*two*superincreasing**knapsacks*is given by the facets*of*the individual*knapsack*polytopes. ...##
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On lexicographic approximations of integer programs
[article]

2017
*
arXiv
*
pre-print

We use the

arXiv:1610.06470v3
fatcat:jwqazyg3vnh3bhbfwjaj7tzngu
*lexicographic**order*to define a hierarchy*of*primal*and*dual bounds on the optimum*of*a bounded integer program. ... The latter result implies a stronger polyhedral representation for the integer feasible points*and*a new approach for deriving strong valid inequalities to the integer*hull*. ... Thus the*superincreasing*property is sufficient for a*knapsack*to be a lex-*ordered*set. ...##
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Scanning integer points with lex-inequalities: a finite cutting plane algorithm for integer programming with linear objective

2020
*
4OR
*

To each integer point x in K we associate a family

doi:10.1007/s10288-020-00459-6
fatcat:s57tueauundszdnm7qfarj74su
*of*inequalities (lex-inequalities) that define the*convex**hull**of*the integer points in K that are not*lexicographically*smaller than x. ... AbstractWe consider the integer points in a unimodular cone K*ordered*by a*lexicographic*rule defined by a lattice basis. ... We thank both*of*them. We are also grateful to Akshay Gupte for his constructive comments*and*his pointers to the existing literature. ...##
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Scanning integer points with lex-inequalities: A finite cutting plane algorithm for integer programming with linear objective
[article]

2020
*
arXiv
*
pre-print

To each integer point x in K we associate a family

arXiv:1811.02345v2
fatcat:hmfu2hilizcnvce4cip3ijv4zi
*of*inequalities (lex-cuts) that defines the*convex**hull**of*the integer points in K that are not*lexicographically*smaller than x. ... We consider the integer points in a unimodular cone K*ordered*by a*lexicographic*rule defined by a lattice basis. ... We thank both*of*them. We are also grateful to Akshay Gupte for his constructive comments*and*his pointers to the existing literature. ...##
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On Dantzig figures from graded lexicographic orders

2018
*
Discrete Mathematics
*

We construct two families

doi:10.1016/j.disc.2018.02.016
fatcat:tix5g3kf5jbtfpvgjeyh5mtlcu
*of*Dantzig figures, which are (d,2d)-polytopes with an antipodal vertex pair, from*convex**hulls**of*initial subsets for the graded*lexicographic*(grlex)*and*graded reverse*lexicographic*... (grevlex)*orders*on Z^d_≥ 0. ... Q) yields the*convex**hull**of*all the integral vectors that belong to a standard integral simplex*and*are*lexicographically*smaller (resp. greater) than a fixed integer vector. ...##
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Exact Lexicographic Scheduling and Approximate Rescheduling
[article]

2020
*
arXiv
*
pre-print

Further, we revisit state-

arXiv:1805.03437v3
fatcat:x6f632viijfhrpsireri7ugaim
*of*-the-art exact*lexicographic*optimization methods*and*propose a*lexicographic*branch-*and*-bound algorithm whose performance is validated computationally. ... Our approach is substantiated analytically, with a price*of*robustness characterization parameterized by the degree*of*uncertainty,*and*numerically. ...*Convex**hulls**of**superincreasing**knapsacks**and**lexicographic**orderings*. Discrete Applied Mathematics, 201 , 150-163. [29] Hanasusanto, G. A., Kuhn, D., & Wiesemann, W. (2015). ...##
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Limits to parallel computation: P-completeness theory

1996
*
ChoiceReviews
*

This book is an introduction to the rapidly growing theory

doi:10.5860/choice.33-3959
fatcat:qjoueeu225gr7jvwdf6gkoxfbq
*of*Pcompleteness -the branch*of*complexity theory that focuses on identifying the "hardest" problems in the class P*of*problems solvable in polynomial ... That is, algorithm designers have failed to find NC algorithms, feasible highly parallel solutions that take time polynomial in the logarithm*of*the problem size while using only a polynomial number*of*... Acknowledgments The numbers in parentheses at the end*of*each entry in the bibliography are the page numbers on which that item is referenced. ...##
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Subject Index to Volumes 1–75

2001
*
Information Processing Letters
*

, 1468, 1536, 1997, 2762,
3092, 3219

doi:10.1016/s0020-0190(01)00175-2
fatcat:5y67tfm6yfbblakrus5nnhs73e
*ordering*, 974, 1162*lexicographic*path*ordering*, 2437 constraints, 2666*lexicographic*relation, 506 semicommutations, 1468*lexicographical*, 684, 970 metrics ... , 1528 topological*order*problem, 1873*lexicographically*greatest string, 3844 least circular substrings, 576*lexicographically*minimal maximal path, 1332 strings, 3988*lexicographically**ordered*... subregion, 46 vertex, 1777 unimodality, 1676 , 1777*of**convex*polygons, 1676 Subject Index / Information Processing Letters 78 (2001 ) 5-336 unimonotone polygon, 2426 uninterpreted, 2879 parallel system ...