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Graph matching (GM), as a longstanding problem in computer vision and pattern recognition, still suffers from numerous cluttered outliers in practical applications. To address this issue, we present the zero-assignment constraint (ZAC) for…

Computer Vision and Pattern Recognition · Computer Science 2020-03-27 Fudong Wang , Nan Xue , Jin-Gang Yu , Gui-Song Xia

Given a graph G, a matching is a subset of edges of G that do not share an endpoint. A matching M is uniquely restricted if the subgraph induced by the endpoints of the edges of M has exactly one perfect matching. Given a graph G and a…

Data Structures and Algorithms · Computer Science 2025-08-19 Juhi Chaudhary , Ignasi Sau , Meirav Zehavi

Graph matching pairs corresponding nodes across two or more graphs. The problem is difficult as it is hard to capture the structural similarity across graphs, especially on large graphs. We propose to incorporate high-order information for…

Artificial Intelligence · Computer Science 2020-10-12 Hui Xu , Liyao Xiang , Youmin Le , Xiaoying Gan , Yuting Jia , Luoyi Fu , Xinbing Wang

For a graph $G=(V,E),$ a matching $M$ is a set of independent edges. The topic of matchings is well studied in graph theory. In this paper many varieties of matchings are discussed.

Combinatorics · Mathematics 2018-05-10 Todd Fenstermacher , Soumendra Ganguly , Stephen Hedetniemi , Renu Laskar

The graph homomorphism problem (HOM) asks whether the vertices of a given $n$-vertex graph $G$ can be mapped to the vertices of a given $h$-vertex graph $H$ such that each edge of $G$ is mapped to an edge of $H$. The problem generalizes the…

Data Structures and Algorithms · Computer Science 2015-02-20 Fedor V. Fomin , Alexander Golovnev , Alexander S. Kulikov , Ivan Mihajlin

We study the design of fixed-parameter algorithms for problems already known to be solvable in polynomial time. The main motivation is to get more efficient algorithms for problems with unattractive polynomial running times. Here, we focus…

Computational Complexity · Computer Science 2021-01-06 Archontia C. Giannopoulou , George B. Mertzios , Rolf Niedermeier

We consider straight line drawings of a planar graph $G$ with possible edge crossings. The \emph{untangling problem} is to eliminate all edge crossings by moving as few vertices as possible to new positions. Let $fix(G)$ denote the maximum…

Computational Geometry · Computer Science 2011-11-14 Alexander Ravsky , Oleg Verbitsky

Binary jumbled pattern matching asks to preprocess a binary string $S$ in order to answer queries $(i,j)$ which ask for a substring of $S$ that is of length $i$ and has exactly $j$ 1-bits. This problem naturally generalizes to…

Data Structures and Algorithms · Computer Science 2014-07-01 Travis Gagie , Danny Hermelin , Gad M. Landau , Oren Weimann

We investigate the space complexity of certain perfect matching problems over bipartite graphs embedded on surfaces of constant genus (orientable or non-orientable). We show that the problems of deciding whether such graphs have (1) a…

Computational Complexity · Computer Science 2010-04-29 Samir Datta , Raghav Kulkarni , Raghunath Tewari , N. V. Vinodchandran

Let $G=(V, E)$ be a given edge-weighted graph and let its {\em realization} $\mathcal{G}$ be a random subgraph of $G$ that includes each edge $e \in E$ independently with probability $p$. In the {\em stochastic matching} problem, the goal…

Data Structures and Algorithms · Computer Science 2020-04-21 Soheil Behnezhad , Mahsa Derakhshan

We prove that unless the Exponential Time Hypothesis (ETH) fails, deciding if there is a homomorphism from graph $G$ to graph $H$ cannot be done in time $|V(H)|^{o(|V(G)|)}$. We also show an exponential-time reduction from Graph…

Data Structures and Algorithms · Computer Science 2016-02-17 Marek Cygan , Fedor V. Fomin , Alexander Golovnev , Alexander S. Kulikov , Ivan Mihajlin , Jakub Pachocki , Arkadiusz Socała

We investigate the tractability of a simple fusion of two fundamental structures on graphs, a spanning tree and a perfect matching. Specifically, we consider the following problem: given an edge-weighted graph, find a minimum-weight…

Data Structures and Algorithms · Computer Science 2024-07-12 Kristóf Bérczi , Tamás Király , Yusuke Kobayashi , Yutaro Yamaguchi , Yu Yokoi

Finding paths in graphs is a fundamental graph-theoretic task. In this work, we we are concerned with finding a path with some constraints on its length and the number of vertices neighboring the path, that is, being outside of and incident…

Computational Complexity · Computer Science 2019-05-28 Max-Jonathan Luckow , Till Fluschnik

We investigate the parameterized complexity of the recognition problem for the proper $H$-graphs. The $H$-graphs are the intersection graphs of connected subgraphs of a subdivision of a multigraph $H$, and the properness means that the…

Computational Complexity · Computer Science 2020-11-25 Steven Chaplick , Petr A. Golovach , Tim A. Hartmann , Dušan Knop

Random graph matching refers to recovering the underlying vertex correspondence between two random graphs with correlated edges; a prominent example is when the two random graphs are given by Erd\H{o}s-R\'{e}nyi graphs $G(n,\frac{d}{n})$.…

Machine Learning · Statistics 2020-07-21 Jian Ding , Zongming Ma , Yihong Wu , Jiaming Xu

In this work we consider two two-criteria optimization problems: given an input graph, the goal is to find its interval (or chordal) supergraph that minimizes the number of edges and its clique number simultaneously. For the interval…

Discrete Mathematics · Computer Science 2021-01-19 Dariusz Dereniowski , Adam Stański

Recently, deep learning based methods have demonstrated promising results on the graph matching problem, by relying on the descriptive capability of deep features extracted on graph nodes. However, one main limitation with existing deep…

Computer Vision and Pattern Recognition · Computer Science 2021-03-16 Quankai Gao , Fudong Wang , Nan Xue , Jin-Gang Yu , Gui-Song Xia

This paper formulates a necessary and sufficient condition for a generic graph matching problem to be equivalent to the maximum vertex and edge weight clique problem in a derived association graph. The consequences of this results are…

Artificial Intelligence · Computer Science 2009-12-24 Brijnesh Jain , Klaus Obermayer

For every integer $g$, isomorphism of graphs of Euler genus at most $g$ can be decided in linear time. This improves previously known algorithms whose time complexity is $n^{O(g)}$ (shown in early 1980's), and in fact, this is the first…

Data Structures and Algorithms · Computer Science 2015-11-10 Ken-ichi Kawarabayashi

We study the perfect matching reconfiguration problem: Given two perfect matchings of a graph, is there a sequence of flip operations that transforms one into the other? Here, a flip operation exchanges the edges in an alternating cycle of…

Data Structures and Algorithms · Computer Science 2019-04-15 Marthe Bonamy , Nicolas Bousquet , Marc Heinrich , Takehiro Ito , Yusuke Kobayashi , Arnaud Mary , Moritz Mühlenthaler , Kunihiro Wasa