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We propose a dual decomposition and linear program relaxation of the NP -hard minimum cost multicut problem. Unlike other polyhedral relaxations of the multicut polytope, it is amenable to efficient optimization by message passing. Like…

Data Structures and Algorithms · Computer Science 2017-01-13 Paul Swoboda , Bjoern Andres

In this work, we propose an optimization framework for estimating a sparse robust one-dimensional subspace. Our objective is to minimize both the representation error and the penalty, in terms of the l1-norm criterion. Given that the…

Machine Learning · Statistics 2024-03-07 Xiao Ling , Paul Brooks

We introduce a particular optimization problem that minimizes the sum of a non-convex quadratic function and logarithmic barrier-functions in a $\ell_\infty$-trust-region (i.e. cube). Our paper covers three topics. We explain the relevance…

Numerical Analysis · Mathematics 2018-06-20 Martin Neuenhofen

In this paper we consider the coupled task scheduling problem with exact delay times on a single machine with the objective of minimizing the total completion time of the jobs. We provide constant-factor approximation algorithms for several…

Optimization and Control · Mathematics 2024-05-03 David Fischer , Péter Györgyi

In the area of parameterized complexity, to cope with NP-Hard problems, we introduce a parameter k besides the input size n, and we aim to design algorithms (called FPT algorithms) that run in O(f(k)n^d) time for some function f(k) and…

Data Structures and Algorithms · Computer Science 2013-07-19 Yoichi Iwata , Keigo Oka , Yuichi Yoshida

We propose simple polynomial-time algorithms for two linear conic feasibility problems. For a matrix $A\in \mathbb{R}^{m\times n}$, the kernel problem requires a positive vector in the kernel of $A$, and the image problem requires a…

Optimization and Control · Mathematics 2019-04-09 Daniel Dadush , László A. Végh , Giacomo Zambelli

Many problems in optimization theory are strongly nonlinear in the traditional sense but possess a hidden linear structure over suitable idempotent semirings. After an overview of `Idempotent Mathematics' with an emphasis on matrix theory,…

Numerical Analysis · Mathematics 2025-10-20 Grigori Litvinov , Andrei Sobolevskii

Reducing the conditions under which a given set satisfies the stipulations of the subset sum proposition to a set of linear relationships, the question of whether a set satisfies subset sum may be answered in a polynomial number of steps by…

Data Structures and Algorithms · Computer Science 2017-05-16 Aubrey Alston

This article discusses ability of Linear Programming models to be used as solvers of NP-complete problems. Integer Linear Programming is known as NP-complete problem, but non-integer Linear Programming problems can be solved in polynomial…

Computational Complexity · Computer Science 2025-10-20 Radoslaw Hofman

We study shared multi-processor scheduling problem where each job can be executed on its private processor and simultaneously on one of many processors shared by all jobs in order to reduce the job's completion time due to processing time…

Discrete Mathematics · Computer Science 2021-03-05 Dariusz Dereniowski , Wieslaw Kubiak

Allen's interval algebra is one of the most well-known calculi in qualitative temporal reasoning with numerous applications in artificial intelligence. Recently, there has been a surge of improvements in the fine-grained complexity of…

Computational Complexity · Computer Science 2023-05-26 Leif Eriksson , Victor Lagerkvist

There exist several results on deciding termination and computing runtime bounds for triangular weakly non-linear loops (twn-loops). We show how to use results on such subclasses of programs where complexity bounds are computable within…

Logic in Computer Science · Computer Science 2024-11-19 Nils Lommen , Fabian Meyer , Jürgen Giesl

The 0-1 linear programming problem with nonnegative constraint matrix and objective vector e origins from many NP-hard combinatorial optimization problems. In this paper, we consider recovering an optimal solution to the problem from a…

Optimization and Control · Mathematics 2022-12-09 Meijia Han , Wenxing Zhu

We consider the energy minimization problem for undirected graphical models, also known as MAP-inference problem for Markov random fields which is NP-hard in general. We propose a novel polynomial time algorithm to obtain a part of its…

Artificial Intelligence · Computer Science 2015-08-19 Paul Swoboda , Alexander Shekhovtsov , Jörg Hendrik Kappes , Christoph Schnörr , Bogdan Savchynskyy

The intention of this note is two-fold. First, we study integer optimization problems in standard form defined by $A \in\mathbb{Z}^{m\times{}n}$ and present an algorithm to solve such problems in polynomial-time provided that both the…

Optimization and Control · Mathematics 2016-04-01 Stephan Artmann , Friedrich Eisenbrand , Christoph Glanzer , Timm Oertel , Santosh Vempala , Robert Weismantel

We consider the hardness of approximation of optimization problems from the point of view of definability. For many NP-hard optimization problems it is known that, unless P = NP, no polynomial-time algorithm can give an approximate solution…

Logic in Computer Science · Computer Science 2019-08-30 Albert Atserias , Anuj Dawar

In this paper, we address the problem of minimizing a convex function f over a convex set, with the extra constraint that some variables must be integer. This problem, even when f is a piecewise linear function, is NP-hard. We study an…

Optimization and Control · Mathematics 2012-09-05 Michel Baes , Timm Oertel , Christian Wagner , Robert Weismantel

The question if a given partial solution to a problem can be extended reasonably occurs in many algorithmic approaches for optimization problems. For instance, when enumerating minimal dominating sets of a graph $G=(V,E)$, one usually…

Computational Complexity · Computer Science 2018-10-11 Katrin Casel , Henning Fernau , Mehdi Khosravian Ghadikolaei , Jérôme Monnot , Florian Sikora

Information inequalities appear in many database applications such as query output size bounds, query containment, and implication between data dependencies. Recently Khamis et al. proposed to study the algorithmic aspects of information…

Databases · Computer Science 2023-09-22 Miika Hannula

Given a system model where machines have distinct speeds and power ratings but are otherwise compatible, we consider various problems of scheduling under resource constraints on the system which place the restriction that not all machines…

Data Structures and Algorithms · Computer Science 2019-02-08 Mohammed Haroon Dupty , Pragati Agrawal , Shrisha Rao