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Related papers: PTAS for Sparse General-Valued CSPs

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We study the computational complexity of exact minimisation of rational-valued discrete functions. Let $\Gamma$ be a set of rational-valued functions on a fixed finite domain; such a set is called a finite-valued constraint language. The…

Computational Complexity · Computer Science 2016-09-22 Johan Thapper , Stanislav Zivny

Consider the problem of minimizing the sum of two convex functions, one being smooth and the other non-smooth. In this paper, we introduce a general class of approximate proximal splitting (APS) methods for solving such minimization…

Optimization and Control · Mathematics 2014-04-23 Mojtaba Kadkhodaie , Maziar Sanjabi , Zhi-Quan Luo

The Computational Singular Perturbation (CSP) method of Lam and Goussis is an iterative method to reduce the dimensionality of systems of ordinary differential equations with multiple time scales. In [J. Nonlin. Sci., to appear], the…

Dynamical Systems · Mathematics 2016-09-07 Antonios Zagaris , Hans G. Kaper , Tasso J. Kaper

The Promise Constraint Satisfaction Problem (PCSP) is a generalization of the Constraint Satisfaction Problem (CSP) that includes approximation variants of satisfiability and graph coloring problems. Barto [LICS '19] has shown that a…

Computational Complexity · Computer Science 2025-06-09 Kristina Asimi , Libor Barto

In this paper, we propose a general framework to design {efficient} polynomial time approximation schemes (EPTAS) for fundamental stochastic combinatorial optimization problems. Given an error parameter $\epsilon>0$, such algorithmic…

Data Structures and Algorithms · Computer Science 2025-05-30 Danny Segev , Sahil Singla

Binary quadratic programming problems have attracted much attention in the last few decades due to their potential applications. This type of problems are NP-hard in general, and still considered a challenge in the design of efficient…

Data Structures and Algorithms · Computer Science 2014-11-20 Khaled Elbassioni , Trung Thanh Nguyen

We develop faster approximation algorithms for Metric-TSP building on recent, nearly linear time approximation schemes for the LP relaxation [Chekuri and Quanrud, 2017]. We show that the LP solution can be sparsified via cut-sparsification…

Data Structures and Algorithms · Computer Science 2018-02-06 Chandra Chekuri , Kent Quanrud

We present two algorithms for the minimum feedback vertex set problem in planar graphs: an $O(n \log n)$ PTAS using a linear kernel and balanced separator, and a heuristic algorithm using kernelization and local search. We implemented these…

Data Structures and Algorithms · Computer Science 2018-04-24 Glencora Borradaile , Hung Le , Baigong Zheng

The complexity of the promise constraint satisfaction problem $\operatorname{PCSP}(\mathbf{A},\mathbf{B})$ is largely unknown, even for symmetric $\mathbf{A}$ and $\mathbf{B}$, except for the case when $\mathbf{A}$ and $\mathbf{B}$ are…

Computational Complexity · Computer Science 2024-08-19 Tamio-Vesa Nakajima , Stanislav Živný

A discrete temporal constraint satisfaction problem is a constraint satisfaction problem (CSP) whose constraint language consists of relations that are first-order definable over $(\Bbb Z,<)$. Our main result says that every distance CSP is…

Logic · Mathematics 2016-04-27 Manuel Bodirsky , Barnaby Martin , Antoine Mottet

In this paper, we study the \emph{sparse integer least squares problem} (SILS), an NP-hard variant of least squares with sparse $\{0, \pm 1\}$-vectors. We propose an $\ell_1$-based SDP relaxation, and a randomized algorithm for SILS, which…

Optimization and Control · Mathematics 2026-05-19 Alberto Del Pia , Dekun Zhou

Standard quadratic optimization problems (StQPs) provide a versatile modelling tool in various applications. In this paper, we consider StQPs with a hard sparsity constraint, referred to as sparse StQPs. We focus on various tractable convex…

Optimization and Control · Mathematics 2023-10-09 Immanuel Bomze , Bo Peng , Yuzhou Qiu , E. Alper Yıldırım

Partitioning the vertices of a graph into two roughly equal parts while minimizing the number of edges crossing the cut is a fundamental problem (called Balanced Separator) that arises in many settings. For this problem, and variants such…

Computational Complexity · Computer Science 2015-03-20 Venkatesan Guruswami , Ali Kemal Sinop , Yuan Zhou

We study the efficient approximability of basic graph and logic problems in the literature when instances are specified hierarchically as in \cite{Le89} or are specified by 1-dimensional finite narrow periodic specifications as in…

Computational Complexity · Computer Science 2007-05-23 Madhav V. Marathe , Harry B. Hunt , Richard E. Stearns , Venkatesh Radhakrishnan

A $\mu$-constrained Boolean Max-CSP$(\psi)$ instance is a Boolean Max-CSP instance on predicate $\psi:\{0,1\}^r \to \{0,1\}$ where the objective is to find a labeling of relative weight exactly $\mu$ that maximizes the fraction of satisfied…

Data Structures and Algorithms · Computer Science 2023-08-21 Suprovat Ghoshal , Euiwoong Lee

Consider the Maximum Weight Independent Set problem for rectangles: given a family of weighted axis-parallel rectangles in the plane, find a maximum-weight subset of non-overlapping rectangles. The problem is notoriously hard both in the…

Data Structures and Algorithms · Computer Science 2016-11-22 Michał Pilipczuk , Erik Jan van Leeuwen , Andreas Wiese

We study the Travelling Salesperson (TSP) and the Steiner Tree problem (STP) in graphs of low highway dimension. This graph parameter was introduced by Abraham et al. [SODA 2010] as a model for transportation networks, on which TSP and STP…

Data Structures and Algorithms · Computer Science 2019-07-15 Yann Disser , Andreas Emil Feldmann , Max Klimm , Jochen Konemann

The purpose of this work is to introduce and characterize the Bounded Acceleration Shortest Path (BASP) problem, a generalization of the Shortest Path (SP) problem. This problem is associated to a graph: the nodes represent positions of a…

Data Structures and Algorithms · Computer Science 2024-04-10 Stefano Ardizzoni , Luca Consolini , Mattia Laurini , Marco Locatelli

The Constraint-satisfaction problem (CSP) is fundamental in mathematics, physics, and theoretical computer science. Continuous local search (CLS) solvers, as recent advancements, can achieve highly competitive results on certain classes of…

Artificial Intelligence · Computer Science 2026-01-29 Yunuo Cen , Zixuan Wang , Jintao Zhang , Zhiwei Zhang , Xuanyao Fong

In this paper, we develop a parameterized proximal point algorithm (P-PPA) for solving a class of separable convex programming problems subject to linear and convex constraints. The proposed algorithm is provable to be globally convergent…

Optimization and Control · Mathematics 2018-12-11 Jianchao Bai , Hongchao Zhang , Jicheng Li