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11th International Conference on algorithms and Discrete Applied Mathematics, CALDAM 2025

作者： Madani, Amirali Maheshwari, Anil Miraftab, Babak Roy, Bodhayan Carleton University OttawaON Canada IIT Kharagpur Kharagpur India

ISBN: (纸本)9783031834370

A connected graph has a (k,)-cover if each of its edges is contained in at least cliques of order k. Motivated by recent advances in extremal combinatorics and the literature on edge modification problems, we study the algorithmic version of the (3, 1)-cover problem. Given a connected graph G, the (k, 1)-cover problem is to find the minimum number of non-edges of G, whose addition to G yields a graph with a (k, 1)-cover. We show that the (3, 1)-cover problem is NP-complete for general graphs. Moreover, we show that it admits no polynomial-time constant-factor approximation algorithm unless P=NP. However, we show that the (3, 1)-cover problem can be solved in polynomial time when the input graph is chordal. © The Author(s), under exclusive license to Springer Nature Switzerland AG 2025.

关键词： graph algorithms

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Monte Carlo graph Coloring

arXiv

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arXiv 2025年

作者： Cazenave, Tristan Negrevergne, Benjamin Sikora, Florian Université Paris-Dauphine PSL University CNRS LAMSADE Paris75016 France

graph Coloring is probably one of the most studied and famous problem in graph algorithms. Exact methods fail to solve instances with more than few hundred vertices, therefore, a large number of heuristics have been proposed. Nested Monte Carlo Search (NMCS) and Nested Rollout Policy Adaptation (NRPA) are Monte Carlo search algorithms for single player games. Surprisingly, few work has been dedicated to evaluating Monte Carlo search algorithms to combinatorial graph problems. In this paper we expose how to efficiently apply Monte Carlo search to graph Coloring and compare this approach to existing ones. © 2025, CC BY-NC-ND.

关键词： graph algorithms

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GENERALIZED graph CODES AND THIER MINIMUM DISTANCES

arXiv

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arXiv 2025年

作者： Fujii, Naoki Graduate School of Fundamental Science and Engineering Waseda University Japan

graph code is a linear code obtained from linear codes C and a certain bipartite graph G. In this paper, I propose an expansion of the definition of graph code to general -partite, and give its lower bound of minimum distance. I also give an example of generalized graph code and calculate its parameters [n, k, d]. Copyright © 2025, The Authors. All rights reserved.

关键词： graph algorithms

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Twin-Width One 42

Twin-Width One

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42nd International Symposium on Theoretical Aspects of Computer Science, STACS 2025

作者： Ahn, Jungho Jacob, Hugo Köhler, Noleen Paul, Christophe Reinald, Amadeus Wiederrecht, Sebastian Seoul Korea Republic of LIRMM Université de Montpellier CNRS Montpellier France University of Leeds United Kingdom School of Computing KAIST Daejeon Korea Republic of

ISBN: (纸本)9783959773652

We investigate the structure of graphs of twin-width at most 1, and obtain the following results: graphs of twin-width at most 1 are permutation graphs. In particular they have an intersection model and a linear structure. There is always a 1-contraction sequence closely following a given permutation diagram. Based on a recursive decomposition theorem, we obtain a simple algorithm running in linear time that produces a 1-contraction sequence of a graph, or guarantees that it has twin-width more than 1. We characterise distance-hereditary graphs based on their twin-width and deduce a linear time algorithm to compute optimal sequences on this class of graphs. © Jungho Ahn, Hugo Jacob, Noleen Köhler, Christophe Paul, Amadeus Reinald, and Sebastian Wiederrecht.

关键词： graph algorithms

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SDG_HHAG Framework: Homogeneous and Heterogeneous Attributed graphs 12th

SDG_HHAG Framework: Homogeneous and Heterogeneous Attribute...

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12th International Conference on Big Data and Artificial Intelligence, BDA 2024

作者： Sandhya Rani, A. Ashwitha, G. Swarupa Rani, K. University of Hyderabad Telangana Hyderabad India

ISBN: (纸本)9783031818202

graphs, comprising nodes, edges, and additional information known as attributed graphs, are essential for many applications which represents the complex data structures. Accessing these types of graphs is a significant challenge due to privacy concerns and the sensitivity of information. In addition, finding the attributed graphs with different node types and edge types is another challenge. Lack of attributed graph datasets with its heterogeneity factors hinders the powerful graph analysis algorithms across different fields. To address these challenges, we propose the SDG_HHAG Framework, a Synthetic Data Generation Framework comprising two approaches: 1) Synt_HoAG (Synthetic Homogeneous Attributed graphs) to enrich existing graphs with node and edge attributes, and 2) Synt_HeAG (Synthetic Heterogeneous Attributed graphs) to create and generate synthetic heterogeneous attributed graphs. We conducted experiments using the proposed approaches, and results reveal that these approaches are flexible to generate the synthetic graphs with attributes which are useful for graph analytics. Further, generated synthetic datasets are used for applications of social networks such as community detection and for the applications of routing problem such as query reachability. © The Author(s), under exclusive license to Springer Nature Switzerland AG 2025.

关键词： graph algorithms

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A Bayesian Perspective on Uncertainty Quantification for Estimated graph Signals

arXiv

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arXiv 2025年

作者： Rompelberg, Lennard Schaub, Michael T. Department of Computer Science RWTH Aachen University Aachen Germany

We present a Bayesian perspective on quantifying the uncertainty of graph signals estimated or reconstructed from imperfect observations. We show that many conventional methods of graph signal estimation, reconstruction and imputation, can be reinterpreted as finding the mean of a posterior Gaussian distribution, with a covariance matrix shaped by the graph structure. In this perspective, assumptions of signal smoothness as well as bandlimitedness are naturally expressible as the choice of certain prior distributions;noisy, noise-free or partial observations are expressible in terms of certain likelihood models. In addition to providing a point estimate, as most standard estimation strategies do, our probabilistic framework enables us to characterize the shape of the estimated signal distribution around the estimate in terms of the posterior covariance matrix. © 2025, CC BY.

关键词： graph algorithms

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Polynomial-Time algorithms for Path Cover on Trees and graphs of Bounded Treewidth 11th

Polynomial-Time Algorithms for Path Cover on Trees and Gr...

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11th International Conference on algorithms and Discrete Applied Mathematics, CALDAM 2025

作者： Foucaud, Florent Majumder, Atrayee Mömke, Tobias Roshany-Tabrizi, Aida CNRS Clermont Auvergne INP Mines Saint-Étienne LIMOS Clermont-Ferrand63000 France University of Augsburg Augsburg Germany

ISBN: (纸本)9783031834370

In the Path Cover problem, one asks to cover the vertices of a graph using the smallest possible number of (not necessarily disjoint) paths. While the variant where the paths need to be pairwise vertex-disjoint, which we call Path Partition, is extensively studied, surprisingly little is known about Path Cover. We start filling this gap by designing a linear-time algorithm for Path Cover on trees. Let t be the treewidth of a given graph. We then show that Path Cover can be solved in polynomial time on graphs of bounded treewidth, in XP time ntO(t), using a dynamic programming scheme. Our algorithm gives an FPT 2O(tlogt)n algorithm for Path Partition as a corollary. These results also apply to the variants where the paths are required to be induced (i.e. chordless) and/or edge-disjoint. © The Author(s), under exclusive license to Springer Nature Switzerland AG 2025.

关键词： graph algorithms

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Approximate Anchored Densest Subgraph Search on Large Static and Dynamic graphs 51st

Approximate Anchored Densest Subgraph Search on Large Static...

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51st International Conference on Very Large Data Bases, VLDB 2025

作者： Zhang, Qi Li, Rong-Hua Zhang, Yalong Wang, Guoren University of Science and Technology Beijing Beijing China Beijing Institute of Technology Beijing China

Densest subgraph search, aiming to identify a subgraph with maximum edge density, faces limitations as the edge density inadequately reflects biases towards a given vertex set R. To address this, the R-subgraph density was introduced, refining the doubled edge density by penalizing vertices in a subgraph but not in R, using the degree as a penalty factor. This advancement leads to the Anchored Densest Subgraph (ADS) search problem, which finds the subgraph Š with the highest R-subgraph density for a given set R. Nonetheless, current algorithms for ADS search face significant inefficiencies in handling large-scale graphs or the sizable R set. Furthermore, these algorithms require re-computing the ADS whenever the graph is updated, complicating the efficient maintenance within dynamic graphs. To tackle these challenges, we propose the concept of integer R-subgraph density and study the problem of finding a subgraph S ⊆ V with the highest integer R-subgraph density. We reveal that the R-subgraph density of S provides an additive approximation to that of ADS with a difference of less than 1, and hence S is termed the Approximate Anchored Densest Subgraph (AADS). For searching the AADS, we present an efficient global algorithm incorporating the re-orientation network flow technique and binary search, operating in a time polynomial to the graph's size. Additionally, we propose a novel local algorithm using shortest-path-based methods for the max-flow computation from s to t around R, markedly boosting performance in scenarios with larger R sets. For dynamic graphs, both basic and improved algorithms are developed to efficiently maintain the AADS when an edge is updated. Extensive experiments and a case study demonstrate the efficiency, scalability, and effectiveness of our solutions. © 2025, VLDB Endowment, All rights reserved.

关键词： graph algorithms

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Open Problems and Recent Developments on a Complexity Framework for Forbidden Subgraphs 50th

Open Problems and Recent Developments on a Complexity Fra...

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50th International Conference on Current Trends in Theory and Practice of Computer Science, SOFSEM 2025

作者： van Leeuwen, Erik Jan Department Information and Computing Sciences Utrecht University Utrecht Netherlands

ISBN: (纸本)9783031826696

For any finite set H={H1,…,Hp} of graphs, a graph is H-subgraph-free if it does not contain any of H1,…,Hp as a subgraph. In this invited talk, I discuss a recently proposed algorithmic meta classification that precisely classifies if certain problems (sharing specific properties) are "efficiently solvable" or "computationally hard" for H-subgraph-free graphs, depending on H. For a broad set of classic graph problems, this framework yields a dichotomy (depending on H) between polynomial-time solvability and NP-completeness. For other problems, like computing the diameter of a graph, it gives a dichotomy between almost-linear-time solvability and having no subquadratic-time algorithm (conditioned on some hardness hypotheses). This paper discusses this framework, highlights current developments and open problems, and surveys recent insights into the complexity on H-subgraph-free graphs of problems that do not fall within the framework. © The Author(s), under exclusive license to Springer Nature Switzerland AG 2025.

关键词： graph algorithms

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Cluster Editing on Cographs and Related Classes 42

Cluster Editing on Cographs and Related Classes

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42nd International Symposium on Theoretical Aspects of Computer Science, STACS 2025

作者： Lafond, Manuel Sánchez, Alitzel L. Luo, Weidong Department of Computer Science Université de Sherbrooke Canada

ISBN: (纸本)9783959773652

In the Cluster Editing problem, sometimes known as (unweighted) Correlation Clustering, we must insert and delete a minimum number of edges to achieve a graph in which every connected component is a clique. Owing to its applications in computational biology, social network analysis, machine learning, and others, this problem has been widely studied for decades and is still undergoing active research. There exist several parameterized algorithms for general graphs, but little is known about the complexity of the problem on specific classes of graphs. Among the few important results in this direction, if only deletions are allowed, the problem can be solved in polynomial time on cographs, which are the P4-free graphs. However, the complexity of the broader editing problem on cographs is still open. We show that even on a very restricted subclass of cographs, the problem is NP-hard, W[1]-hard when parameterized by the number p of desired clusters, and that time no(p/log p) is forbidden under the ETH. This shows that the editing variant is substantially harder than the deletion-only case, and that hardness holds for the many superclasses of cographs (including graphs of clique-width at most 2, perfect graphs, circle graphs, permutation graphs). On the other hand, we provide an almost tight upper bound of time nO(p), which is a consequence of a more general nO(cw·p) time algorithm, where cw is the clique-width. Given that forbidding P4s maintains NP-hardness, we look at {P4,C4}-free graphs, also known as trivially perfect graphs, and provide a cubic-time algorithm for this class. © Manuel Lafond, Alitzel López Sánchez, and Weidong Luo.

关键词： graph algorithms

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