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The Intersection of Knapsack Polyhedra and Extensions
[chapter]

1998
*
Lecture Notes in Computer Science
*

For

doi:10.1007/3-540-69346-7_19
fatcat:hskhjhcxzvb65akofiqjglmbri
*the**intersection**of*several*knapsack**polyhedra*, incomparabilities between*the*column vectors*of**the*associated matrix will be shown to transfer into inequalities*of**the*associated polyhedron. ...*The*scheme is related to Chvatal-Gomory cutting planes*and*important special cases such as odd hole*and*clique inequalities for*the*stable set polyhedron or families*of*inequalities for*the**knapsack*polyhedron ... We try to go one step further*and*investigate*the**intersection**of*two or more*knapsack**polyhedra*. ...##
###
Page 3481 of Mathematical Reviews Vol. , Issue 91F
[page]

1991
*
Mathematical Reviews
*

*The*author discusses

*the*connections with max flow min cut properties

*and*provides a subadditive characterization

*of*

*the*facets

*of*

*the*underlying

*polyhedra*. ...

*The*problem

*of*maximizing a concave integer function over a set

*of*integer points

*of*a polymatroid

*intersection*is transformed to a problem

*of*maximizing a linear function over an

*intersection*

*of*

*the*same ...

##
###
Page 5955 of Mathematical Reviews Vol. , Issue 2000h
[page]

2000
*
Mathematical Reviews
*

Xue Liang Li (PRC-NWP-AM; Xian)
2000h:90066 90C27 90C10 90C57 Martin, Alexander (D-KOZU; Berlin); Weismantel, Robert (D-KOZU,; Berlin)

*The**intersection**of**knapsack**polyhedra**and**extensions*. ...*The*authors address*the*question*of*when*the*facets*of*a single*knapsack*polyhedron define strong cutting planes*of*an integer program when several*knapsack*constraints*intersect*. ...##
###
Page 10498 of Mathematical Reviews Vol. , Issue 2004m
[page]

2004
*
Mathematical Reviews
*

It is shown that

*the*standard*and*primal separation problems are equivalent (in*the*Karp sense) for set packing, set covering, set partitioning*and**knapsack**polyhedra*, for general integer pro- grams,*and*... Summary: “By solving a constrained matroid*intersection*prob- lem, we give a matroid generalization*of**the*stable theorem*of*Gale*and*Shapley. ...##
###
A Principled Approach to Mixed Integer/Linear Problem Formulation
[chapter]

2009
*
Operations Research and Cyber-Infrastructure
*

We view mixed integer/linear problem formulation as a process

doi:10.1007/978-0-387-88843-9_5
fatcat:jgwqjdtgurgwbpcsjkrf7r3icu
*of*identifying disjunctive*and**knapsack*constraints in a problem*and*converting them to mixed integer form. ... We show through a series*of*examples that following this process can yield mixed integer models that automatically incorporate some*of**the*modeling devices that have been discovered over*the*years for ...*The*proof is a straightforward*extension**of*Jeroslow's proof [4] . ...##
###
Page 2061 of Mathematical Reviews Vol. , Issue 84e
[page]

1984
*
Mathematical Reviews
*

It is shown that integral polymatroids have SID,

*polyhedra*defined by totally unimodular matrices have MID,*and*branching*polyhedra*as well as*intersections**of*two strongly-base-orderable matroids have ...*Extensive*computational tests have confirmed*the*efficiency*of*this approach for a wide variety*of*problems with as many as 5000 variables.” Baum, S.; Trotter, L. ...##
###
On the existence of compact ϵ-approximated formulations for knapsack in the original space
[article]

2015
*
arXiv
*
pre-print

We show that there exists a family

arXiv:1503.04717v1
fatcat:v4c57ytzofaknohgxmf4hmf2rq
*of**Knapsack*polytopes such that, for each polytope P from this family*and*each ϵ > 0, any ϵ-approximated formulation*of*P in*the*original space R^n requires a number ... This answers a question by Bienstock*and*McClosky (2012). ...*Knapsack*has been*extensively*studied in*the*combinatorial optimization*and*integer programming communities (see e.g. [9, 12] ). ...##
###
Randomized complexity of linear arrangements and polyhedra?
[chapter]

1999
*
Lecture Notes in Computer Science
*

We survey some

doi:10.1007/3-540-48321-7_1
fatcat:yatxihz3m5dl3c3254i44m2tfy
*of**the*recent results on*the*complexity*of*recognizing n{dimensional linear arrangements*and*convex*polyhedra*by randomized algebraic decision trees. ... In particular, we derive rst nontrivial, in fact quadratic, randomized lower bounds on*the*problems like*Knapsack**and*Bounded Integer Programming. ... We shall deal here with*the*randomized complexity*of*linear arrangements,*and*convex*polyhedra*. ...##
###
Page 4595 of Mathematical Reviews Vol. , Issue 94h
[page]

1994
*
Mathematical Reviews
*

A consequence is

*the*existence*of*a strongly polynomial nonuniform algorithm for*the*NP-complete*knapsack*problem. ... two re- sults: (i)*the*minimum number*of*simplices for a vertex-preserving triangulation*of*J; is 67,*and*(ii)*the*minimum number*of*sim- 52B_ Polytopes*and**polyhedra*94n:52029 plices for a vertex-preserving ...##
###
Traces of the XII Aussois Workshop on Combinatorial Optimization

2010
*
Mathematical programming
*

Here is a brief glimpse

doi:10.1007/s10107-010-0369-3
fatcat:b7slvsqv4ncy7j45l3u4dcilz4
*of**the*content*of*these papers. "Separation Algorithms for 0-1*Knapsack*Polytopes" by Konstantinos Kaparis,*and*Adam N. ... Therefore, attention is focused on*the*former;*extensive*computational experiments are conducted to evaluate*the*efficiency*and*fairness achieved with it. ...##
###
Linear and combinatorial sharing problems

1986
*
Discrete Applied Mathematics
*

.,

doi:10.1016/0166-218x(86)90022-3
fatcat:elyksmaouje5hbmzhmkk6hzv6i
*the*minimization*of*separable objectives f(x)= max{~(xj) ]j-1 ..... n} on*polyhedra*from linear*and*combinatorial optimization. ... Finiteness*and*efficiency is derived for several applications, in particular on submodular flow*and*matching*polyhedra*. ... Submodular flows generalize network flows as well as polymatroid*intersections*. ...##
###
ZERO: Playing Mathematical Programming Games
[article]

2021
*
arXiv
*
pre-print

We provide an overview

arXiv:2111.07932v2
fatcat:hpm3p6vx5rgvbjhdf73kh53bz4
*of**the*software's key components*and*showcase a*Knapsack*Game, i.e., a game where each player solves a binary*knapsack*problem. ... We present ZERO, a modular*and**extensible*C++ library interfacing Mathematical Programming*and*Game Theory. ... Acknowledgements This work has been supported by*the*Canada Excellence Research Chair in Real-time Decision-making (DS4DM). ...##
###
Improved Approximation Algorithms for Matroid and Knapsack Median Problems and Applications

2016
*
ACM Transactions on Algorithms
*

open an independent set

doi:10.1145/2963170
fatcat:guvwv2lubrfphemtq2l7l7vduu
*of*facilities*and*assign clients to open facilities so as to minimize*the*sum*of**the*facility-opening*and*client-connection costs. ... Our techniques also yield an improvement for*the**knapsack*median problem. ... I thank Chandra Chekuri for some useful discussions regarding*the*matroid-*intersection*median problem. ...##
###
Page 5224 of Mathematical Reviews Vol. , Issue 2000g
[page]

2000
*
Mathematical Reviews
*

Lenstra, Solving a linear Diophantine equation with lower

*and*upper bounds on*the*variables (229-242); Alexander Martin*and*Robert Weismantel,*The**intersection**of**knapsack**polyhedra**and**extensions*(243 ... They prove*the*continuous differentiability*of*L(s, S)*and**the*existence*of*an interior minimiser*and*even though*the*minimisers might not satisfy*the*conditions assumed,*the*proof*of**the*optimality*of*...##
###
The subdivision of large simplicial cones in Normaliz
[article]

2016
*
arXiv
*
pre-print

In

arXiv:1605.07440v1
fatcat:o72ouxkhiffhrno3ojevbeybsu
*the*homogeneous case, in which*the*polyhedron is a cone,*the*set*of*generators is*the*Hilbert basis*of**the**intersection**of**the*cone*and**the*lattice, an affine monoid. ... Normaliz is an open-source software for*the*computation*of*lattice points in rational*polyhedra*, or, in a different language,*the*solutions*of*linear diophantine systems. ... Introduction Normaliz [3] is a software for*the*computation*of*lattice points in rational*polyhedra*. ...
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