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Inspired by notorious combinatorial optimization problems on graphs, in this paper we consider a series of related problems defined using a metric space and topology determined by a graph. Particularly, we present the Independent Set,…

Combinatorics · Mathematics 2025-07-30 Alexander Grigoriev , Katherine Faulkner

A consistent path system in a graph $G$ is an intersection-closed collection of paths, with exactly one path between any two vertices in $G$. We call $G$ metrizable if every consistent path system in it is the system of geodesic paths…

Combinatorics · Mathematics 2023-11-17 Maria Chudnovsky , Daniel Cizma , Nati Linial

We analyze a minimal model of a growing network. At each time step, a new vertex is added; then, with probability delta, two vertices are chosen uniformly at random and joined by an undirected edge. This process is repeated for t time…

Statistical Mechanics · Physics 2009-11-07 Duncan S. Callaway , John E. Hopcroft , Jon M. Kleinberg , M. E. J. Newman , Steven H. Strogatz

A new efficient algorithm is presented for finding all simple cycles that satisfy a length constraint in a directed graph. When the number of vertices is non-trivial, most cycle-finding problems are of practical interest for sparse graphs…

Data Structures and Algorithms · Computer Science 2021-05-27 Anshul Gupta , Toyotaro Suzumura

We study how we can accelerate the spreading of information in temporal graphs via shifting operations; a problem that captures real-world applications varying from information flows to distribution schedules. In a temporal graph there is a…

Data Structures and Algorithms · Computer Science 2025-10-09 Argyrios Deligkas , Eduard Eiben , George Skretas

A \emph{temporal graph} is, informally speaking, a graph that changes with time. When time is discrete and only the relationships between the participating entities may change and not the entities themselves, a temporal graph may be viewed…

Discrete Mathematics · Computer Science 2015-03-03 Othon Michail

For a simple graph $G$, the $2$-distance graph, $D_2(G)$, is a graph with the vertex set $V(G)$ and two vertices are adjacent if and only if their distance is $2$ in the graph $G$. In this paper, we characterize all graphs with connected…

Combinatorics · Mathematics 2023-07-04 S. H. Jafari , S. R. Musawi

Many optimization problems can be naturally represented as (hyper) graphs, where vertices correspond to variables and edges to tasks, whose cost depends on the values of the adjacent variables. Capitalizing on the structure of the graph,…

Logic in Computer Science · Computer Science 2015-04-13 Nicklas Hoch , Ugo Montanari , Matteo Sammartino

Graph is an important data representation which appears in a wide diversity of real-world scenarios. Effective graph analytics provides users a deeper understanding of what is behind the data, and thus can benefit a lot of useful…

Artificial Intelligence · Computer Science 2018-02-05 Hongyun Cai , Vincent W. Zheng , Kevin Chen-Chuan Chang

The complexity of a reasoning task over a graphical model is tied to the induced width of the underlying graph. It is well-known that the conditioning (assigning values) on a subset of variables yields a subproblem of the reduced complexity…

Data Structures and Algorithms · Computer Science 2012-07-19 Bozhena Bidyuk , Rina Dechter

We consider the problem of finding a subgraph of a given graph minimizing the sum of given functions at vertices evaluated at their subgraph degrees. While the problem is NP-hard already for bipartite graphs when the functions are convex on…

Optimization and Control · Mathematics 2021-04-27 Gabriel Deza , Shmuel Onn

Over the past decade, we witness an increasing amount of interest in the design of exact exponential-time and parameterized algorithms for problems in Graph Drawing. Unfortunately, we still lack knowledge of general methods to develop such…

Data Structures and Algorithms · Computer Science 2023-10-10 Siddharth Gupta , Guy Sa'ar , Meirav Zehavi

A transitive graph is 2-dimensional if it can be represented as the intersection of two linear orders. Such representations make answering of reachability queries trivial, and allow many problems that are NP-hard on arbitrary graphs to be…

Discrete Mathematics · Computer Science 2019-04-09 Henning Koehler

Transformers have revolutionized the field of machine learning. In particular, they can be used to solve complex algorithmic problems, including graph-based tasks. In such algorithmic tasks a key question is what is the minimal size of a…

Machine Learning · Computer Science 2026-01-29 Gilad Yehudai , Clayton Sanford , Maya Bechler-Speicher , Orr Fischer , Ran Gilad-Bachrach , Amir Globerson

Many different classification tasks need to manage structured data, which are usually modeled as graphs. Moreover, these graphs can be dynamic, meaning that the vertices/edges of each graph may change during time. Our goal is to jointly…

Machine Learning · Computer Science 2019-08-20 Franco Manessi , Alessandro Rozza , Mario Manzo

In this work we study the topological properties of temporal hypergraphs. Hypergraphs provide a higher dimensional generalization of a graph that is capable of capturing multi-way connections. As such, they have become an integral part of…

Computational Geometry · Computer Science 2023-02-07 Audun Myers , Cliff Joslyn , Bill Kay , Emilie Purvine , Gregory Roek , Madelyn Shapiro

Reachability is the problem of deciding whether there is a path from one vertex to the other in the graph. Standard graph traversal algorithms such as DFS and BFS take linear time to decide reachability however their space complexity is…

Computational Complexity · Computer Science 2019-02-06 Rahul Jain , Raghunath Tewari

Graphs are commonly used to represent objects, such as images and text, for pattern classification. In a dynamic world, an object may continuously evolve over time, and so does the graph extracted from the underlying object. These changes…

Data Structures and Algorithms · Computer Science 2017-06-14 Haishuai Wang

We investigate the computational complexity of separating two distinct vertices s and z by vertex deletion in a temporal graph. In a temporal graph, the vertex set is fixed but the edges have (discrete) time labels. Since the corresponding…

Computational Complexity · Computer Science 2020-10-12 Till Fluschnik , Hendrik Molter , Rolf Niedermeier , Malte Renken , Philipp Zschoche

The problem of counting occurrences of query graphs in a large data graph, known as subgraph counting, is fundamental to several domains such as genomics and social network analysis. Many important special cases (e.g. triangle counting)…

Distributed, Parallel, and Cluster Computing · Computer Science 2016-04-05 Venkatesan T. Chakaravarthy , Michael Kapralov , Prakash Murali , Fabrizio Petrini , Xinyu Que , Yogish Sabharwal , Baruch Schieber