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In this paper, we consider the problem of scheduling an application on a parallel computational platform. The application is a particular task graph, either a linear chain of tasks, or a set of independent tasks. The platform is made of…

Data Structures and Algorithms · Computer Science 2012-10-18 Guillaume Aupy , Anne Benoit

This paper is about how to partition decision variables while decomposing a large-scale optimization problem for the best performance of distributed solution methods. Solving a large-scale optimization problem sequen- tially can be…

Optimization and Control · Mathematics 2017-10-26 Yuchen Zheng , Ilbin Lee , Nicoleta Serban

We study the problem of edge partitioning, where the goal is to partition the edge set of a graph into several parts. The replication factor of a vertex $v$ is the number of parts that contain edges incident to $v$. The goal is to minimize…

Discrete Mathematics · Computer Science 2026-05-08 Alexander Yakunin , Andrey Kupavskii , Alexander Sushin , Stanislav Moiseev

An exact algorithm is presented for solving edge weighted graph partitioning problems. The algorithm is based on a branch and bound method applied to a continuous quadratic programming formulation of the problem. Lower bounds are obtained…

Optimization and Control · Mathematics 2009-12-10 William Hager , Dzung Phan , Hongchao Zhang

Partitioning a graph into blocks of "roughly equal" weight while cutting only few edges is a fundamental problem in computer science with a wide range of applications. In particular, the problem is a building block in applications that…

Data Structures and Algorithms · Computer Science 2021-05-06 Lars Gottesbüren , Tobias Heuer , Peter Sanders , Christian Schulz , Daniel Seemaier

The submodular partitioning problem asks to minimize, over all partitions $P$ of a ground set $V$, the sum of a given submodular function $f$ over the parts of $P$. The problem has seen considerable work in approximability, as it…

Data Structures and Algorithms · Computer Science 2025-07-03 Kristóf Bérczi , Karthekeyan Chandrasekaran , Tamás Király , Daniel P. Szabo

In the Two-Bar Charts Packing Problem (2-BCPP), it is required to pack the bar charts (BCs) consisting of two bars into the horizontal unit-height strip of minimal length. The bars may move vertically within the strip, but it is forbidden…

Discrete Mathematics · Computer Science 2021-06-23 Adil Erzin , Georgii Melidi , Stepan Nazarenko , Roman Plotnikov

We construct an asymptotic approximation to the solution of a transmission problem for a body containing a region occupied by many small inclusions. The cluster of inclusions is characterised by two small parameters that determine the…

Analysis of PDEs · Mathematics 2016-07-22 Michael Nieves

The message complexity of a distributed algorithm is the total number of messages sent by all nodes over the course of the algorithm. This paper studies the message complexity of distributed algorithms for fundamental graph optimization…

Distributed, Parallel, and Cluster Computing · Computer Science 2023-11-28 Fabien Dufoulon , Shreyas Pai , Gopal Pandurangan , Sriram V. Pemmaraju , Peter Robinson

In the regime of bounded transportation costs, additive approximations for the optimal transport problem are reduced (rather simply) to relative approximations for positive linear programs, resulting in faster additive approximation…

Data Structures and Algorithms · Computer Science 2018-10-23 Kent Quanrud

Optimization under uncertainty deals with the problem of optimizing stochastic cost functions given some partial information on their inputs. These problems are extremely difficult to solve and yet pervade all areas of technological and…

Statistical Mechanics · Physics 2015-03-13 Fabrizio Altarelli , Alfredo Braunstein , Abolfazl Ramezanpour , Riccardo Zecchina

We study the problem of approximating the level set of an unknown function by sequentially querying its values. We introduce a family of algorithms called Bisect and Approximate through which we reduce the level set approximation problem to…

Statistics Theory · Mathematics 2021-02-24 François Bachoc , Tommaso Cesari , Sébastien Gerchinovitz

Many discrete optimization problems amount to selecting a feasible set of edges of least weight. We consider in this paper the context of spatial graphs where the positions of the vertices are uncertain and belong to known uncertainty sets.…

Data Structures and Algorithms · Computer Science 2022-09-27 Marin Bougeret , Jérémy Omer , Michael Poss

We study the shared processor scheduling problem with a single shared processor where a unit time saving (weight) obtained by processing a job on the shared processor depends on the job. A polynomial-time optimization algorithm has been…

Discrete Mathematics · Computer Science 2021-01-19 Dariusz Dereniowski , Wieslaw Kubiak

In this paper we consider the classic scheduling problem of minimizing total weighted completion time on unrelated machines when jobs have release times, i.e, $R | r_{ij} | \sum_j w_j C_j$ using the three-field notation. For this problem, a…

Data Structures and Algorithms · Computer Science 2016-06-29 Sungjin Im , Shi Li

We present a time-optimal deterministic distributed algorithm for approximating a minimum weight vertex cover in hypergraphs of rank $f$. This problem is equivalent to the Minimum Weight Set Cover Problem in which the frequency of every…

Distributed, Parallel, and Cluster Computing · Computer Science 2018-08-20 Ran Ben-Basat , Guy Even , Ken-ichi Kawarabayashi , Gregory Schwartzman

One of the most useful measures of cluster quality is the modularity of a partition, which measures the difference between the number of the edges joining vertices from the same cluster and the expected number of such edges in a random…

Data Analysis, Statistics and Probability · Physics 2009-09-29 Hristo Djidjev

We formalize the problem of selecting the optimal set of options for planning as that of computing the smallest set of options so that planning converges in less than a given maximum of value-iteration passes. We first show that the problem…

Artificial Intelligence · Computer Science 2019-03-19 Yuu Jinnai , David Abel , D Ellis Hershkowitz , Michael Littman , George Konidaris

We consider a natural generalization of classical scheduling problems in which using a time unit for processing a job causes some time-dependent cost which must be paid in addition to the standard scheduling cost. We study the scheduling…

Data Structures and Algorithms · Computer Science 2018-12-03 Lin Chen , Nicole Megow , Roman Rischke , Leen Stougie , José Verschae

Resource allocation problems in many computer systems can be formulated as mathematical optimization problems. However, finding exact solutions to these problems using off-the-shelf solvers in an online setting is often intractable for…

Distributed, Parallel, and Cluster Computing · Computer Science 2021-04-15 Deepak Narayanan , Fiodar Kazhamiaka , Firas Abuzaid , Peter Kraft , Matei Zaharia