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Compact LP Relaxations for Allocation Problems *

Klaus Jansen, Lars Rohwedder
BY 1st Symposium on Simplicity in Algorithms   unpublished
With an instantiation for each objective function, we prove the bounds for the new compact LP relaxation (in particular, for the configuration LP).  ...  Our main result is a new LP relaxation for these problems. This LP has only O(n 3) variables and constraints.  ...  S O S A 2 0 1 8 11:12 Compact LPs for Allocation Problems Proof. As before, let denote the current length of L.  ... 
fatcat:752srlkcj5dqjan3gej3l72n5i

Page 48 of The Journal of the Operational Research Society Vol. 52, Issue 1 [page]

2001 The Journal of the Operational Research Society  
The basic idea is to relax all but a specific set of constraints. We solve this relaxed problem.  ...  In our research, we applied the concept of relaxation developed by Geoffrion” and presented by Lasdon* to develop a methodology for solving linear preemptive goal programming problems.  ... 

A cutting-plane method for contiguity-constrained spatial aggregation

Johannes Oehrlein, Jan-Henrik Haunert
2017 Journal of Spatial Information Science  
In this article we present a new exact method for area aggregation and compare it with a state-of-the-art method for the same problem.  ...  Even simple problem variants are known to be NP-hard, meaning that there is no reasonable hope for an efficient exact algorithm.  ...  time an LP relaxation is solved optimally.  ... 
doi:10.5311/josis.2017.15.379 fatcat:sxs2cy3cbnchnjvrqwcde37msm

Cooperative facility location games

Michel X. Goemans, Martin Skutella
2004 Journal of Algorithms  
We establish strong connections between fair cost allocations and linear programming relaxations for several variants of the facility location problem.  ...  In particular, we show that a fair cost allocation exists if and only if there is no integrality gap for a corresponding linear programming relaxation; this was only known for the simplest unconstrained  ...  Acknowledgments The authors are much indebted to Michel Le Breton for motivating them to study facility location problems from a game-theoretic point of view and for numerous interesting and helpful discussions  ... 
doi:10.1016/s0196-6774(03)00098-1 fatcat:guuroo2hqngn5f7r24tqijkhpq

On Approximate Welfare- and Revenue-Maximizing Equilibria for Size-Interchangeable Bidders [article]

Enrique Areyan Viqueira, Amy Greenwald, Victor Naroditskiy
2017 arXiv   pre-print
Instead of computing an outcome that simultaneously yields an allocation and corresponding prices, one could first solve for an allocation that respects a reserve price, and then solve for a corresponding  ...  time, given a fixed allocation.  ...  allocation is given as input; likewise for, LP Greedy Utilitarian and LP Greedy Egalitarian.  ... 
arXiv:1708.03097v1 fatcat:ml5l7ake4raz3hyrwtni4a6nt4

Multiarmed Bandit Problems with Delayed Feedback [article]

Sudipto Guha and Kamesh Munagala and Martin Pal
2013 arXiv   pre-print
This arises naturally in allocation problems which have been studied extensively in the literature, albeit in the absence of delays in the feedback. We study this problem in the Bayesian setting.  ...  We show that bandit problems with delayed feedback that arise in allocation settings can be forced to have significant structure, with a slight loss in optimality.  ...  At a high level, our algorithm starts with the standard LP relaxation to the problem [6, 18] .  ... 
arXiv:1011.1161v3 fatcat:ai6lglbumvbshorbaktbsmtd4a

Resource Allocation for Full-Duplex Relay-Assisted Device-to-Device Multicarrier Systems

Shuping Dang, Justin P. Coon, Gaojie Chen
2017 IEEE Wireless Communications Letters  
By this way, the resource allocation for UGs can be carried out by a small amount of computational overhead.  ...  This paper analyzes the resource allocation problem for full-duplex relay-assisted device-to-device (D2D) multicarrier systems, where multiple D2D user groups (UGs) coexist in an underlaying manner.  ...  (MBIP) problem (for the allocation of subcarriers).  ... 
doi:10.1109/lwc.2017.2647806 fatcat:emsowas2kvda7h6gbiz4fk6bp4

Modeling and efficient optimization for object-based scalability and some related problems

P. Batra
2000 IEEE Transactions on Image Processing  
We show that for this problem the duality gap for Lagrange and LP relaxations is exactly the same.  ...  Unlike previous approaches to solve the operational bit-allocation problem using Lagrangean relaxation, we discuss an algorithm that solves linear programming (LP) relaxation of this problem.  ...  However, we are not aware of prior use of LP relaxations of this problem for signal compression. Before proceeding with the outline, we contrast LP and Lagrange relaxations.  ... 
doi:10.1109/83.869179 pmid:18262907 fatcat:om5xfxcgojaorcccy4bht6lpnq

Near-Optimal and Robust Mechanism Design for Covering Problems with Correlated Players [article]

Hadi Minooei, Chaitanya Swamy
2016 arXiv   pre-print
For single-dimensional settings, this black-box reduction applies even when we only have an LP-relative approximation algorithm for the algorithmic problem.  ...  We consider the problem of designing incentive-compatible, ex-post individually rational (IR) mechanisms for covering problems in the Bayesian setting, where players' types are drawn from an underlying  ...  Acknowledgments We thank the anonymous reviewers and referees of the conference and journal submissions for various useful comments.  ... 
arXiv:1311.6883v2 fatcat:gozlnpbpynatdjhxcf57bkst2q

Near-Optimal and Robust Mechanism Design for Covering Problems with Correlated Players [chapter]

Hadi Minooei, Chaitanya Swamy
2013 Lecture Notes in Computer Science  
For singledimensional settings, this black-box reduction applies even when we only have an LP-relative approximation algorithm for the algorithmic problem.  ...  However, certain difficulties arise in achieving this goal for covering problems (see "Differences . . . packing problems" below).  ...  Acknowledgments We thank the anonymous reviewers and referees of the conference and journal submissions for various useful comments.  ... 
doi:10.1007/978-3-642-45046-4_31 fatcat:b4bjkbmstjdrvejirv4hszugxe

Towards Efficient Large-Scale Network Slicing: An LP Rounding-and-Refinement Approach [article]

Wei-Kun Chen, Ya-Feng Liu, Fan Liu, Yu-Hong Dai, Zhi-Quan Luo
2022 arXiv   pre-print
We show that compared with a natural LP relaxation of the MILP formulation, the novel LP relaxation is much more compact in terms of smaller numbers of variables and constraints, and much stronger in terms  ...  The problem has been formulated as a mixed integer linear programming (MILP) formulation in the literature. We first propose a novel linear programming (LP) relaxation of the MILP formulation.  ...  Acknowledgments We would like to thank the two anonymous reviewers for their insightful comments.  ... 
arXiv:2107.14404v2 fatcat:n56uzayo4bhm5jgblwdqkk2xwu

Strong bounds with cut and column generation for class-teacher timetabling

Haroldo Gambini Santos, Eduardo Uchoa, Luiz Satoru Ochi, Nelson Maculan
2010 Annals of Operations Research  
This work presents an integer programming formulation for a variant of the Class-Teacher Timetabling problem, which considers the satisfaction of teacher preferences and also the proper distribution of  ...  Therefore, a cut and column generation algorithm to solve its linear relaxation is provided.  ...  We thank the anonymous referees for their constructive comments, leading to an improved version of the paper.  ... 
doi:10.1007/s10479-010-0709-y fatcat:kmdkax3cgrfjdbnkbplkvexilq

Improved Throughput for All-or-Nothing Multicommodity Flows with Arbitrary Demands [article]

Anya Chaturvedi, Chandra Chekuri, Andréa W. Richa, Mattias Rost, Stefan Schmid, Jamison Weber
2021 arXiv   pre-print
(INFOCOM'19) that allows for easy solving via standard LP solvers.  ...  On the theoretical side we obtain substantially improved bi-criteria approximation algorithms for this NP-hard problem.  ...  In fact, (5) is crucial to establish the "equivalence" between the LP relaxation of the ANF packing formulation (Figure 1b(b) ) and the LP relaxation of the compact edge-flow MIP.  ... 
arXiv:2005.04533v6 fatcat:bk2y7e3bzvc4jjlkrmns67wr3e

A Primal Decomposition Method with Suboptimality Bounds for Distributed Mixed-Integer Linear Programming

Andrea Camisa, Ivano Notarnicola, Giuseppe Notarstefano
2018 2018 IEEE Conference on Decision and Control (CDC)  
Agents repeatedly update local allocation vectors, which converge to an optimal resource allocation of an approximate version of the original problem.  ...  MILPs are NPhard problems and several challenges arise in a distributed framework, so that looking for suboptimal solutions is of interest.  ...  Thus, we adopt a relaxation approach similar to the one proposed for the LP approximation.  ... 
doi:10.1109/cdc.2018.8619597 dblp:conf/cdc/CamisaNN18 fatcat:r2ygjybpafbe5cnub44wlzeqtm

Near-Optimal and Robust Mechanism Design for Covering Problems with Correlated Players

Hadi Minooei, Chaitanya Swamy
2015 ACM Transactions on Economics and Computation  
For singledimensional settings, this black-box reduction applies even when we only have an LP-relative approximation algorithm for the algorithmic problem.  ...  However, certain difficulties arise in achieving this goal for covering problems (see "Differences . . . packing problems" below).  ...  Acknowledgments We thank the anonymous reviewers and referees of the conference and journal submissions for various useful comments.  ... 
doi:10.1145/2790133 fatcat:ntaxe67pi5ad7khcf62qu3olga
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