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In the design of greedy algorithms for the maximum cardinality matching problem the utilization of degree information when selecting the next edge is a well established and successful approach. We define the class of "degree sensitive"…

Data Structures and Algorithms · Computer Science 2016-12-21 Bert Besser , Bastian Werth

Motivated by the pervasiveness of strong inapproximability results for Max-CSPs, we introduce a relaxed notion of an approximate solution of a Max-CSP. In this relaxed version, loosely speaking, the algorithm is allowed to replace the…

Computational Complexity · Computer Science 2012-04-26 Per Austrin , Johan Håstad

We propose a theoretical framework to capture incremental solutions to cardinality constrained maximization problems. The defining characteristic of our framework is that the cardinality/support of the solution is bounded by a value…

Discrete Mathematics · Computer Science 2018-04-18 Aaron Bernstein , Yann Disser , Martin Groß

This paper studies lower bounds for fundamental optimization problems in the CONGEST model. We show that solving problems exactly in this model can be a hard task, by providing $\tilde{\Omega}(n^2)$ lower bounds for cornerstone problems,…

Data Structures and Algorithms · Computer Science 2019-05-27 Nir Bachrach , Keren Censor-Hillel , Michal Dory , Yuval Efron , Dean Leitersdorf , Ami Paz

Designing good error correcting codes whose generator matrix has a support constraint, i.e., one for which only certain entries of the generator matrix are allowed to be non-zero, has found many recent applications, including in distributed…

Information Theory · Computer Science 2018-01-25 Hikmet Yildiz , Babak Hassibi

The problem of finding a maximum $2$-matching without short cycles has received significant attention due to its relevance to the Hamilton cycle problem. This problem is generalized to finding a maximum $t$-matching which excludes specified…

Combinatorics · Mathematics 2023-11-01 Yuni Iwamasa , Yusuke Kobayashi , Kenjiro Takazawa

We investigate the computational complexity of the problem of counting the maximal satisfying assignments of a Constraint Satisfaction Problem (CSP) over the Boolean domain {0,1}. A satisfying assignment is maximal if any new assignment…

Computational Complexity · Computer Science 2016-05-17 Leslie Ann Goldberg , Mark Jerrum

We show a method resulting in the improvement of several polynomial-space, exponential-time algorithms. An instance of the problem Max (r,2)-CSP, or simply Max 2-CSP, is parametrized by the domain size r (often 2), the number of variables n…

Data Structures and Algorithms · Computer Science 2017-11-20 Serge Gaspers , Gregory B. Sorkin

We give a trichotomy theorem for the complexity of approximately counting the number of satisfying assignments of a Boolean CSP instance. Such problems are parameterised by a constraint language specifying the relations that may be used in…

Computational Complexity · Computer Science 2009-07-23 Martin Dyer , Leslie Ann Goldberg , Mark Jerrum

A 2-packing set for an undirected graph $G=(V,E)$ is a subset $\mathcal{S} \subset V$ such that any two vertices $v_1,v_2 \in \mathcal{S}$ have no common neighbors. Finding a 2-packing set of maximum cardinality is a NP-hard problem. We…

Data Structures and Algorithms · Computer Science 2024-02-13 Jannick Borowitz , Ernestine Großmann , Christian Schulz , Dominik Schweisgut

A graph homomorphism is a vertex map which carries edges from a source graph to edges in a target graph. We study the approximability properties of the Weighted Maximum H-Colourable Subgraph problem (MAX H-COL). The instances of this…

Computational Complexity · Computer Science 2008-02-05 Tommy Färnqvist , Peter Jonsson , Johan Thapper

We discuss the computational complexity of approximating maximum a posteriori inference in sum-product networks. We first show NP-hardness in trees of height two by a reduction from maximum independent set; this implies non-approximability…

Artificial Intelligence · Computer Science 2017-09-06 Diarmaid Conaty , Denis D. Mauá , Cassio P. de Campos

Binary polynomial optimization is equivalent to the problem of minimizing a linear function over the intersection of the multilinear set with a polyhedron. Many families of valid inequalities for the multilinear set are available in the…

Optimization and Control · Mathematics 2022-09-13 Rui Chen , Sanjeeb Dash , Oktay Gunluk

In this paper, we propose a randomized $\tilde{O}(\mu(G))$-round algorithm for the maximum cardinality matching problem in the CONGEST model, where $\mu(G)$ means the maximum size of a matching of the input graph $G$. The proposed algorithm…

Distributed, Parallel, and Cluster Computing · Computer Science 2025-01-13 Taisuke Izumi , Naoki Kitamura , Yutaro Yamaguchi

Random $k$-SAT is the single most intensely studied example of a random constraint satisfaction problem. But despite substantial progress over the past decade, the threshold for the existence of satisfying assignments is not known precisely…

Combinatorics · Mathematics 2017-11-29 Amin Coja-Oghlan , Konstantinos Panagiotou

We show that for every positive $\epsilon > 0$, unless NP $\subset$ BPQP, it is impossible to approximate the maximum quadratic assignment problem within a factor better than $2^{\log^{1-\epsilon} n}$ by a reduction from the maximum label…

Computational Complexity · Computer Science 2014-04-01 Konstantin Makarychev , Rajsekar Manokaran , Maxim Sviridenko

In this paper, we provide the first deterministic algorithm that achieves the tight $1-1/e$ approximation guarantee for submodular maximization under a cardinality (size) constraint while making a number of queries that scales only linearly…

Data Structures and Algorithms · Computer Science 2022-04-13 Wenxin Li , Moran Feldman , Ehsan Kazemi , Amin Karbasi

A memory-efficient framework is described for the cardinality-constrained structured data-fitting problem. Dual-based atom-identification rules are proposed that reveal the structure of the optimal primal solution from near-optimal dual…

Optimization and Control · Mathematics 2022-07-21 Zhenan Fan , Huang Fang , Michael P. Friedlander

A mixed dominating set of a graph $G = (V, E)$ is a mixed set $D$ of vertices and edges, such that for every edge or vertex, if it is not in $D$, then it is adjacent or incident to at least one vertex or edge in $D$. The mixed domination…

Data Structures and Algorithms · Computer Science 2019-06-27 Mingyu Xiao

Cardinality-constrained diameter partitioning asks for a partition of $n$ items into two classes of prescribed sizes that minimizes the larger of the two class diameters. We give an $O(n^2)$ algorithm and a matching $\Omega(n^2)$ lower…

Data Structures and Algorithms · Computer Science 2026-05-06 Chao Xu , Mingdong Yang