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New Facets of the Linear Ordering Polytope

1999
*
SIAM Journal on Discrete Mathematics
*

We introduce ten collections

doi:10.1137/s0895480196300145
fatcat:6lvjdfd2qnecxh6omvfcvt3i2a
*of*inequalities representing*facets**of**the*linear ordering*polytope*. ...*The*rotation method for*the*linear ordering*polytope**generalizes**facets*induced by subgraphs called m-fences, M obius ladders and Z m -*facets*introduced by Reinelt 12], (m; k)fences introduced by Bolotashvily ...*The*trivial rotation mapping does not*generate*new*facets*for*the*most known*facets**of**the**polytope*P n , because in many cases*the*mapping*generates*another member*of**the*same*facet*family, i.e.*the*corresponding ...##
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Blending simple polytopes at faces

2004
*
Discrete Mathematics
*

In pursuing

doi:10.1016/j.disc.2004.02.006
fatcat:56tiohr33jem7aryj3gygz65um
*the*Hirsch conjectures, vertex-blends produced*polytopes*which have large diameter and few diametral paths. Here we deÿne and explore blends at higher-dimensional faces. ... Blending two simple*polytopes*together at vertices, at edges, or at other supplementary faces, produces another simple*polytope*. ...*The*truncating hyperplane provides a needed orientation for*the*blend, and it helps avoid admissible-*transformation**problems*. ...##
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Polyhedral results for the edge capacity polytope

2002
*
Mathematical programming
*

In this paper, we investigate

doi:10.1007/s101070200292
fatcat:no7drbxmavgcjciq2hcgsj6rb4
*the**polytopes**of**the**problem*restricted to one arc/edge*of**the*network (*the*undirected/directed edge capacity*problem*) for*the*non-bifurcated*routing*case. ... We give conditions under which*the*inequalities*of**the*edge capacity*polytopes*define*facets**of**the*network loading*polytope*. ... We show that every non-trivial*facet*defining inequality for*the*directed edge capacity*polytope*defines a*facet**of**the*overall network loading*polytope*as well. ...##
###
Generalized multiple depot traveling salesmen problem - polyhedral study and exact algorithm
[article]

2015
*
arXiv
*
pre-print

*The*GMDTSP is an NP-hard

*problem*as it

*generalizes*

*the*MDTSP and has practical applications in design

*of*ring networks, vehicle

*routing*, flexible manufacturing scheduling and postal

*routing*. ...

*The*

*generalized*multiple depot traveling salesmen

*problem*(GMDTSP) is a variant

*of*

*the*multiple depot traveling salesmen

*problem*(MDTSP), where each salesman starts at a distinct depot,

*the*targets are ... We also introduce a

*general*theorem that allows one to lift any

*facet*

*of*

*the*MDTSP

*polytope*into a

*facet*

*of*

*the*GMDTSP

*polytope*. ...

##
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A polyhedral approach to multicommodity survivable network design

1994
*
Numerische Mathematik
*

We discuss basic properties (dimension and trivial

doi:10.1007/s002110050054
fatcat:k4ozr6bzengyfh2usidsabm6ty
*facets*)*of*these*polytopes*in Section 3.*The*remaining part*of**the*paper discusses stronger formulations*of**the**problem*. ... We study properties*of**polytopes*that are naturally associated with*the*model. ...*The**polytope*ICOV(g, b) can be linearly*transformed*into a knapsack*polytope*with*generalized*upper bounds, so all results pertaining to that*polytope*apply also to*the*ICOV-*polytope*. ...##
###
Page 5191 of Mathematical Reviews Vol. , Issue 911
[page]

1991
*
Mathematical Reviews
*

Our result

*generalizes*a result*of*Deza stating that if G is a complete graph with more than two vertices, then an inequality defines a*facet**of*P-(G) if and only if it defines a*facet**of**the*cut*polytope*... We give a sufficient condition for an inequality defining a*facet**of*Pc(G) to define a*facet**of**the*cut*polytope**of*a graph containing G as an induced subgraph. ...##
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Geometric Combinatorics of Transportation Polytopes and the Behavior of the Simplex Method
[article]

2010
*
arXiv
*
pre-print

Transportation

arXiv:1006.2416v1
fatcat:xahucjplsraa3gbzbwkrr2u5ty
*problems*are, in many ways,*the*simplest kind*of*linear programs and thus have a rich combinatorial structure. ... with n*facets*is bounded above by n-d. ... In [82] , Currin studies*the*transportation*problem*with inadmissible*routes*. ...##
###
The m-Cost ATSP
[chapter]

1999
*
Lecture Notes in Computer Science
*

We show that, for m 3 machines, all

doi:10.1007/3-540-48777-8_19
fatcat:oseglnrjyjhcnb4rrmn2n7bm2i
*facets**of**the*one machine subproblem also de ne*facets**of**the*m-ATSP*polytope*. ... We present rst results*of*a polyhedral analysis*of**the*m-ATSP in full*generality*. ... Although there is considerable literature on*the*TSP/ATSP 10, 13{15, 3, 11, 7] as well as on*the*m-ATSP for vehicle*routing*(see 5] and references therein) it seems that*the*m-ATSP*problem*in full*generality*...##
###
The k edge-disjoint 3-hop-constrained paths polytope

2010
*
Discrete Optimization
*

In this paper we consider this

doi:10.1016/j.disopt.2010.05.001
fatcat:44dbxsqhsbcghimhauypucbip4
*problem*from a polyhedral point*of*view. We give an integer programming formulation for*the**problem*and discuss*the*associated*polytope*. ... This*generalizes**the*results*of*Huygens et al. (2004) [1] for k = 2 and L = 2, 3 and those*of*Dahl et al. (2006) [2] for L = 2 and k ≥ 2. This also proves a conjecture in [1] . ... Acknowledgements*The*authors would like to thank*the*anonymous referees for their comments that permitted to considerably improve*the*presentation*of**the*paper. ...##
###
Multiple Depot Ring Star Problem: A polyhedral study and exact algorithm
[article]

2014
*
arXiv
*
pre-print

) assign each non-visited customer to a visited customer or a depot, and (iii) minimize

arXiv:1407.5080v2
fatcat:asvjbja3ifanpixivr4dfhcacq
*the*sum*of**the**routing*costs, i.e.,*the*cost*of**the*cycles and*the*assignment costs. ...*The*Multiple Depot Ring-Star*Problem*(MDRSP) is an important combinatorial optimization*problem*that arises in*the*context*of*optical fiber network design, and in applications pertaining to collecting ...*problem*(MDTSP)*polytope*[6] . ...##
###
Some integer programs arising in the design of main frame computers

1993
*
Mathematical Methods of Operations Research
*

We introduce several relaxations

doi:10.1007/bf01416008
fatcat:iqpxezgkrfhsnbg2cfm7rxluva
*of**the**general*model, which are also N P-hard, but seem to be more easily accessible. ...*The*mathematical relations between*the*relaxations and*the*exact formulation*of**the**problem*are discussed as well. ... Relaxations for*the**General*Model*The*Multiple Knapsack*Problem*In this subsection we present a first relaxation*of**the**general*model. ...##
###
Multiple depot ring star problem: a polyhedral study and an exact algorithm

2016
*
Journal of Global Optimization
*

) assign each non-visited customer to a visited customer or a depot, and (iii) minimize

doi:10.1007/s10898-016-0431-7
fatcat:ryfvtjq5cfhr7fblx6kqfyxoje
*the*sum*of**the**routing*costs, i.e.,*the*cost*of**the*cycles and*the*assignment costs. ...*The*Multiple Depot Ring-Star*Problem*(MDRSP) is an important combinatorial optimization*problem*that arises in*the*context*of*optical fiber network design, and in applications pertaining to collecting ... Lemma 2 is that any valid inequality αx + βy ≤ γ that is*facet*-inducing to*the*MDTSP*polytope*Q and satisfying*the*conditions (1)-(4)*of**the*lemma is valid and*facet*-inducing to*the*MDRSP*polytope*P . ...##
###
Traces of the XII Aussois Workshop on Combinatorial Optimization

2010
*
Mathematical programming
*

"On

doi:10.1007/s10107-010-0369-3
fatcat:b7slvsqv4ncy7j45l3u4dcilz4
*the*Dominant*of**the*s-t-cut*Polytope*" by Martin Skutella, and Alexia Weber gives a complete description*of**the*dominant*of**the*s-t cut*polytope*, by characterizing its vertices,*facets*, and adjacency ... Among other consequences, it permits us to determine whether an integer programming*problem*can be*transformed*to a b-matching*problem*on a bidirected graph, in which case it can be solved using Edmonds ...##
###
Fourier transforms of polytopes, solid angle sums, and discrete volume
[article]

2018
*
arXiv
*
pre-print

Given a real closed

arXiv:1602.08593v2
fatcat:neps7xerjrfhzmrr5bzauxoaem
*polytope*P, we first describe*the*Fourier*transform**of*its indicator function by using iterations*of*Stokes' theorem. ...*The*combinatorics*of**the*face poset*of*P plays a central role in*the*description*of**the*Fourier*transform**of*P. ... Introduction It is a classical*problem*in*the*geometry*of*numbers [30] to find ways*of*counting*the*number*of*lattice points in a*general*convex body. ...##
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A study of the quadratic semi-assignment polytope

2009
*
Discrete Optimization
*

We introduce an isomorphic projection and

doi:10.1016/j.disopt.2008.08.003
fatcat:tdkddlfcbvgjjafecyt6tygtem
*transform**the**polytope*to a tractable full-dimensional*polytope*. ... We study a*polytope*which arises from a mixed integer programming formulation*of**the*quadratic semi-assignment*problem*. ... Acknowledgments*The*authors thank anonymous referees for constructive suggestions for*the*revision*of**the*paper. ...
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