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65th Symposium on Foundations of Computer Science

作者： Byrka, Jaroslaw Grandoni, Fabrizio Traub, Vera Univ Wroclaw Wroclaw Poland USI SUPSI IDSIA Lugano Switzerland Univ Bonn Res Inst Discrete Math Bonn Germany Univ Bonn Hausdorff Ctr Math Bonn Germany

ISBN: (纸本)9798331516758;9798331516741

The Steiner tree problem is one of the most prominent problems in network design. Given an edge-weighted undirected graph and a subset of the vertices, called terminals, the task is to compute a minimum-weight tree containing all terminals (and possibly further vertices). The best-known approximation algorithms for Steiner tree involve enumeration of a (polynomial but) very large number of candidate components and are therefore slow in practice. A promising ingredient for the design of fast and accurate approximation algorithms for Steiner tree is the bidirected cut relaxation (BCR): bidirect all edges, choose an arbitrary terminal as a root, and enforce that each cut containing some terminal but not the root has one unit of fractional edges leaving it. BCR is known to be integral in the spanning tree case [Edmonds'67], i.e., when all the vertices are terminals. For general instances, however, it was not even known whether the integrality gap of BCR is better than the integrality gap of the natural undirected relaxation, which is exactly 2. We resolve this question by proving an upper bound of 1.9988 on the integrality gap of BCR.

关键词： Steiner tree linear programming relaxation integrality gap bidirected cut relaxation

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APPROXIMATING MIN-MEAN-CYCLE FOR LOW-DIAMETER GRAPHS IN NEAR-OPTIMAL TIME AND MEMORY

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SIAM JOURNAL ON OPTIMIZATION 2022年第3期32卷 1791-1816页

作者： Altschuler, Jason M. Parrilo, Pablo A. MIT LIDS 77 Massachusetts Ave Cambridge MA 02139 USA

We revisit Min-Mean-Cycle, the classical problem of finding a cycle in a weighted directed graph with minimum mean weight. Despite an extensive algorithmic literature, previous work failed to achieve a near-linear runtime in the number of edges m. We propose an algorithm with near-linear runtime (O) over tilde (m(W-max/epsilon)(2)) for computing an additive approximation on graphs with polylogarithmic diameter and weights of magnitude at most W-max. In particular, this is the first algorithm whose runtime scales in the number of vertices n as (O) over tilde (n(2)) for the complete graph. Moreover-unconditionally on the diameter-the algorithm uses only O(n) memory beyond reading the input, making it "memory-optimal". Our approach is based on solving a linear programming (LP) relaxation using entropic regularization, which reduces the LP to a Matrix Balancing problem-a la the popular reduction of Optimal Transport to Matrix Scaling. We then round the fractional LP solution using a variant of the classical Cycle-Canceling algorithm that is sped up to near-linear runtime at the expense of being approximate, and implemented in a memory-optimal manner. The algorithm is simple to implement and is competitive with the state-of-the-art methods in practice.

关键词： Min-Mean-Cycle approximation algorithm near-linear runtime linear programming relaxation entropic regularization Matrix Balancing

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A comparison of node-based and arc-based hop-indexed formulations for the Steiner tree problem with hop constraints

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NETWORKS 2022年第2期80卷 178-192页

作者： Fortz, Bernard Gouveia, Luis Moura, Pedro Univ Libre Bruxelles ULB Comp Sci Dept Brussels Belgium INRIA Lille Nord Europe INOCS Villeneuve Dascq France Univ Lisbon Fac Ciencias Dept Estat & Invest Operac Lisbon Portugal CMAFcIO Ctr Matemat Aplicacoes Fundamentais & Inv Lisbon Portugal

We study the relation between the linear programming relaxation of two classes of models for the Steiner tree problem with hop constraints. One class is characterized by having hop-indexed arc variables. Although such models have proved to have a very strong linear programming bound, they are not easy to use because of the huge number of variables. This has motivated some studies with models involving fewer variables that use, instead of the hop-indexed arc variables, hop-indexed node variables. In this article, we contextualize the linear programming relaxation of these node-based models in terms of the linear programming relaxation of known arc-based models. We show that the linear programming relaxation of a general node-based model is implied by the linear programming relaxation of a straightforward arc-based model.

关键词： hop constraint hop-indexed model integer programming linear programming relaxation network design Steiner tree

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Comparison of formulations for the Inventory Routing Problem

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EUROPEAN JOURNAL OF OPERATIONAL RESEARCH 2022年第3期303卷 997-1008页

作者： Archetti, Claudia Ljubic, Ivana ESSEC Business Sch Dept Informat Syst Decis Sci & Stat Cergy Pontoise France

In this paper we propose an analysis and comparison of the strength of the lower bound, measured as the value of the linear programming relaxation, of different formulations for the Inventory Routing Problem (IRP). In particular, we first focus on aggregated formulations, i.e., formulations where variables have no index associated with vehicles, and we analyse the link between compact formulations and their counterparts involving exponentially many constraints. We show that they are equivalent in terms of value of the linear relaxation. In addition, we study the link between aggregated and disaggregated formulations, i.e., formulations where variables have an index related to vehicles. Also in this case, we show that aggregated and disaggregated formulations are equivalent in terms of the value of the corresponding linear relaxation. To the best of our knowledge, this analysis has never been done for the IRP, which instead is gaining a lot of popularity in the literature. Finally, we propose different exact solution approaches based on the aggregated formulations and we compare them with state-of-the-art exact methods for the IRP. Results show that the approaches based on aggregated formulations are competitive in terms of quality of both upper and lower bounds. (C) 2022 The Author(s). Published by Elsevier B.V.

关键词： Routing Inventory routing Aggregated formulation linear programming relaxation Polyhedral projection

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The Gap Function: Evaluating Integer programming Models over Multiple Right-Hand Sides

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OPERATIONS RESEARCH 2022年第2期70卷 1259-1270页

作者： Ajayi, Temitayo Thomas, Christopher Schaefer, Andrew J. Nat Source Improved Plants Ithaca NY 14850 USA Bazean Corp Houston TX 77002 USA Rice Univ Dept Computat & Appl Math Houston TX 77005 USA

For an integer programming model with fixed data, the linear programming relaxation gap is considered one of the most important measures of model quality. There is no consensus, however, on appropriate measures of model quality that account for data variation. In particular, when the right-hand side is not known exactly, one must assess a model based on its behavior over many right-hand sides. Gap functions are the linear programming relaxation gaps parametrized by the right-hand side. Despite drawing research interest in the early days of integer programming, the properties and applications of these functions have been little studied. In this paper, we construct measures of integer programming model quality over sets of right-hand sides based on the absolute and relative gap functions. In particular, we formulate optimization problems to compute the expectation and extrema of gap functions over finite discrete sets and bounded hyperrectangles. These optimization problems are linear programs (albeit of an exponentially large size) that contain at most one special ordered-set constraint. These measures for integer programming models, along with their associated formulations, provide a framework for determining a model's quality over a range of right-hand sides.

关键词： gap function linear programming relaxation modeling superadditive duality

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NMR assignment through linear programming

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JOURNAL OF GLOBAL OPTIMIZATION 2022年第1期83卷 3-28页

作者： Bravo-Ferreira, Jose F. S. Cowburn, David Khoo, Yuehaw Singer, Amit Princeton Univ PACM Princeton NJ 08540 USA Albert Einstein Coll Med Dept Biochem New York NY 10461 USA Albert Einstein Coll Med Dept Physiol New York NY 10461 USA Albert Einstein Coll Med Dept Biophys New York NY 10461 USA Univ Chicago Dept Stat Chicago IL 60637 USA Princeton Univ Dept Math Princeton NJ 08540 USA

Nuclear Magnetic Resonance (NMR) Spectroscopy is the second most used technique (after X-ray crystallography) for structural determination of proteins. A computational challenge in this technique involves solving a discrete optimization problem that assigns the resonance frequency to each atom in the protein. This paper introduces LIAN (linear programming Assignment for NMR), a novel linear programming formulation of the problem which yields state-of-the-art results in simulated and experimental datasets.

关键词： NMR spectroscopy Shortest path problem Resonance assignment problem linear programming relaxation

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linearized Robust Counterparts of Two-Stage Robust Optimization Problems with Applications in Operations Management

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INFORMS JOURNAL ON COMPUTING 2021年第3期33卷 1138-1161页

作者： Ardestani-Jaafari, Amir Delage, Erick Univ British Columbia Fac Management Kelowna BC V1V 1V7 Canada HEC Montreal Dept Decis Sci Montreal PQ H3T 2A7 Canada Grp Res Decis Anal GERAD Montreal PQ Canada

In this article, we discuss an alternative method for deriving conservative approximation models for two-stage robust optimization problems. The method mainly relies on a linearization scheme employed in bilinear programming;therefore, we will say that it gives rise to the linearized robust counterpart models. We identify a close relation between this linearized robust counterpart model and the popular affinely adjustable robust counterpart model. We also describe methods of modifying both types of models to make these approximations less conservative. These methods are heavily inspired by the use of valid linear and conic inequalities in the linearization process for bilinear models. We finally demonstrate how to employ this new scheme in location-transportation and multi-item newsvendor problems to improve the numerical efficiency and performance guarantees of robust optimization.

关键词： two-stage adjustable robust optimization affinely adjustable robust counterpart linear programming relaxation bilinear programming

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A new multicommodity flow model for the job sequencing and tool switching problem

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INTERNATIONAL JOURNAL OF PRODUCTION RESEARCH 2021年第12期59卷 3617-3632页

作者： da Silva, Tiago Tiburcio Chaves, Antonio Augusto Yanasse, Horacio Hideki Univ Fed Sao Paulo Sao Jose Dos Campos Brazil

In this paper a new multicommodity flow mathematical model for the Job Sequencing and Tool Switching Problem (SSP) is presented. The proposed model has an LP relaxation lower bound equal to the number of tools minus the tool machine's capacity. Computational tests were performed comparing the new model with the models of the literature. The proposed model performed better, both in execution time and in the number of instances solved to optimality.

关键词： combinatorial optimisation job sequencing and tool switching multicommodity flow integer programming linear programming relaxation

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An Analysis of the Effects of Renewable Energy Intermittency on the 2030 Korean Electricity Market

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ENERGIES 2023年第10期16卷 4189页

作者： Do, Insu Lee, Siyoung Seo, Gab-Su Kim, Sungsoo Tech Univ Korea TUK Dept Energy & Elect Engn Siheung Si 15073 South Korea Power Syst Engn Ctr Natl Renewable Energy Lab NREL Golden CO USA

Republic of Korea has unique geographical characteristics similar to those of an island, resulting in an isolated power system. For this reason, securing sufficient operating reserves for the system's stability and reliability in the face of the intermittency of increasing variable renewable energy (VRE) is paramount, and this will pave the way to achieving the nation's decarbonization target and carbon neutrality. However, the current reserve-operation method in Republic of Korea does not take into account energy-system conditions, such as the intermittency of the VRE. Therefore, this paper presents an analysis of the impact of changes in reserve-operation methods on the electricity market in the future Republic of Korean power system, with the increased levels of VRE that are currently envisioned. Specifically, three reserve-operation methods, including Korea's current reserve-power-operation standards, were applied to the two power-system plans announced by the Korean government to analyze the annual generator operation and costs. The analysis results show that securing reserves proportional to the VRE would exert negative effects, such as increased power-generation costs and the curtailment of nuclear and VRE generation. These results can contribute to the estimation of operational reserves needed for high levels of VRE and to the design of new the Korean reserve market, to be introduced in 2025.

关键词： carbon neutrality Korean electricity market linear programming relaxation market operation operating reserve variable renewable energy

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A Unified Approach for Resilience and Causal Responsibility with Integer linear programming (ILP) and LP relaxations

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Proceedings of the ACM on Management of Data 2023年第4期1卷 1-27页

作者： Neha Makhija Wolfgang Gatterbauer Northeastern University Boston MA USA

What is a minimal set of tuples to delete from a database in order to eliminate all query answers? This problem is called "the resilience of a query" and is one of the key algorithmic problems underlying various forms of reverse data management, such as view maintenance, deletion propagation and causal responsibility. A long-open question is determining the conjunctive queries (CQs) for which resilience can be solved in *** shed new light on this problem by proposing a unified Integer linear programming (ILP) formulation. It is unified in that it can solve both previously studied restrictions (e.g., self-join-free CQs under set semantics that allow a PTIME solution) and new cases (all CQs under set or bag semantics). It is also unified in that all queries and all database instances are treated with the same approach, yet the algorithm is guaranteed to terminate in PTIME for all known PTIME cases. In particular, we prove that for all known easy cases, the optimal solution to our ILP is identical to a simpler linear programming (LP) relaxation, which implies that standard ILP solvers return the optimal solution to the original ILP in *** approach allows us to explore new variants and obtain new complexity results. 1) It works under bag semantics, for which we give the first dichotomy results in the problem space. 2) We extend our approach to the related problem of causal responsibility and give a more fine-grained analysis of its complexity. 3) We recover easy instances for generally hard queries, including instances with read-once provenance and instances that become easy because of Functional Dependencies in the data. 4) We solve an open conjecture about a unified hardness criterion from PODS 2020 and prove the hardness of several queries of previously unknown complexity. 5) Experiments confirm that our findings accurately predict the asymptotic running times, and that our universal ILP is at times even quicker than a previously proposed dedicated flow al

关键词： causal responsibility dichotomy linear programming relaxation query explanation resilience reverse data management

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