A connected feedback vertex set of a graph is a connected subgraph of the graph whose removal makes the graph cycle free. In this paper, we provide an approximation algorithm for connected feedback vertex set in AT-fr...
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A connected feedback vertex set of a graph is a connected subgraph of the graph whose removal makes the graph cycle free. In this paper, we provide an approximation algorithm for connected feedback vertex set in AT-free graphs. Given an alpha\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\alpha $$\end{document}-approximate solution for feedback vertex set on 2-connected AT-free graph, our algorithm produces a solution of size ((alpha+0.9091)OPT+6)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$((\alpha +0.9091)OPT+6)$$\end{document} for connected feedback vertex set on the same graph. The complexity of our algorithm is O(f(n)+(m+n))\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$O(f(n)+(m+n))$$\end{document}, where the time required to obtain the alpha\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\alpha $$\end{document}-approximate solution is O(f(n)). Our result leads to the following two observations. The optimal feedback vertex set algorithm for AT-free graphs combined with our result provides an algorithm which produces a solution of size (1.9091OPT+6)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddside
A graph is called an induced matching if each vertex in the graph is a degree-1 vertex. The DELETION TO INDUCED MATCHING problem asks whether we can delete at most kvertices from the input graph such that the remainin...
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A graph is called an induced matching if each vertex in the graph is a degree-1 vertex. The DELETION TO INDUCED MATCHING problem asks whether we can delete at most kvertices from the input graph such that the remaining graph is an induced matching. This paper studies parameterized algorithms for this problem by taking the size kof the deletion set as the parameter. First, we prove a 6k-vertex kernel for this problem, improving the previous result of 7k. Second, we give an k*(1.6477k)-time and polynomial-space algorithm, improving the previous running-time bound of k*(1.7485k).
Given a graph G = (V, E ), a function f : V -> { 0 , 1, 2} is said to be a Roman Dominating function if for every v E V with f ( v ) = 0, there exists a vertex u E N ( v ) such that f (u) = 2. A Roman Dominating fu...
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Given a graph G = (V, E ), a function f : V -> { 0 , 1, 2} is said to be a Roman Dominating function if for every v E V with f ( v ) = 0, there exists a vertex u E N ( v ) such that f (u) = 2. A Roman Dominating function f is said to be an Independent Roman Dominating function (or IRDF), if V 1 boolean OR V 2 forms an independent set, where V i = {v E V | f ( v ) = i } , for i E { 0 , 1, 2}. The total weight off is equal to & sum;vEV f ( v ), and is denoted as w ( f ). The Independent Roman Domination Number of G, denoted by iR(G), is defined as min{w(f ) | f is an IRDF of G }. For a given graph G , the problem of computing i R ( G ) is defined as the Minimum Independent Roman Domination problem. The problem is already known to be NP-hard for bipartite graphs. In this paper, we further study the algorithmic complexity of the problem. In this paper, we propose a polynomial-time algorithm to solve the Minimum Independent Roman Domination problem for distance-hereditary graphs, split graphs, and P 4-sparse graphs. (c) 2024 Elsevier B.V. All rights are reserved, including those for text and data mining, AI training, and similar technologies.
The constrained shortest path problem is a fundamental and challenging task in applications built on graphs. In this paper, we formalize and study the Min - Max resource-constrained shortest path ( Min - Max RCSP) pro...
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The constrained shortest path problem is a fundamental and challenging task in applications built on graphs. In this paper, we formalize and study the Min - Max resource-constrained shortest path ( Min - Max RCSP) problem, which generalizes the well-studied Max RCSP problem. The objective is to find a simple path of minimum cost between two query nodes, subject to resource constraints between minimum and maximum limits. This problem has wide applications in fields such as delay networks and transportation. However, we theoretically prove that computing the optimal solution is NP-hard. We propose a two-stage approach that involves resource-based graph reduction followed by cost-guided path generation. To reduce the cost of expensive acyclicity checking, we introduce the technique of ancestor checking based on the shortest path tree. Furthermore, we present an even faster incremental search approach that considers both the path cost and resource constraints while avoiding acyclicity checking. Extensive experiments on twenty real graphs consistently demonstrate the superiority of our proposed methods, achieving up to two orders of magnitude improvement in time efficiency over the baseline algorithms while producing high-quality solutions.
For a fixed graph H, the H-Recoloring problem asks whether, given two homomorphisms from a graph G to H, one homomorphism can be transformed into the other by changing the image of a single vertex in each step and mai...
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For a fixed graph H, the H-Recoloring problem asks whether, given two homomorphisms from a graph G to H, one homomorphism can be transformed into the other by changing the image of a single vertex in each step and maintaining a homomorphism to H throughout. The most general algorithmic result for H-Recoloring so far was proposed by Wrochna in 2014, who introduced a topological approach to obtain a polynomial-time algorithm for any undirected loopless square-free graph H. We show that the topological approach can be used to recover essentially all previous algorithmic results for H-Recoloring and that it is applicable also in the more general setting of digraph homomorphisms. In particular, we show that H-Recoloring admits a polynomial-time algorithm if (i) H is a loopless digraph that does not contain a 4-cycle of algebraic girth 0 and (ii) H is a reflexive digraph that contains no triangle of algebraic girth 1 and no 4-cycle of algebraic girth 0. In both cases, we obtain a polynomial-time algorithm for finding shortest transformations.
In a graph G = (V, E), a non-empty set A of k distinct vertices, is called a k-attack on G. The vertices in the set A are considered to be under attack. A set D subset of V can defend or counter the attack A on G if t...
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In a graph G = (V, E), a non-empty set A of k distinct vertices, is called a k-attack on G. The vertices in the set A are considered to be under attack. A set D subset of V can defend or counter the attack A on G if there exists a one-to-one function f : A bar right arrow D, such that either f (u) = u or there is an edge between u, and its image f (u), in G. A set D is called a k-defensive dominating set if it defends against any k-attack on G. Given a graph G = (V, E), the minimum k-defensive domination problem requires us to compute a minimum cardinality k-defensive dominating set of G. When k is not fixed, it is co-NP-hard to decide if D subset of V is a k-defensive dominating set. However, when k is fixed, the decision version of the problem is NP-complete for general graphs. On the positive side, the problem can be solved in linear time when restricted to paths, cycles, co-chain, and threshold graphs for any k. This paper mainly focuses on the problem when k > 0 is fixed. We prove that the decision version of the problem remains NPcomplete for bipartite graphs;this answers a question asked by Ekim et al. (Discrete Math. 343 (2) (2020)). We establish a lower and upper bound on the approximation ratio for the problem. Further, we show that the minimum k-defensive domination problem is APX-complete for bounded degree graphs. On the positive side, we show that the problem is efficiently solvable for complete bipartite graphs for any k > 0. Towards the end, we study a relationship between the defensive domination number and another well-studied domination parameter. (c) 2024 Elsevier B.V. All rights are reserved, including those for text and data mining, AI training, and similar technologies.
In the r-PSEUDOFOREST DELETION problem, the input is a graph G and integers k, r, and the goal is to decide whether there is a set of at most k vertices whose removal from G results in a graph in which every connected...
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In the r-PSEUDOFOREST DELETION problem, the input is a graph G and integers k, r, and the goal is to decide whether there is a set of at most k vertices whose removal from G results in a graph in which every connected component can be made into a tree by deleting at most redges. In this paper we give an O<^> * ((8r + 1) <^> k) time algorithm for r-PSEUDOFOREST DELETION for every r >= 1.
This research aims to propose a more sophisticated clustering and community detection technique in complex social networks through the use of neural networks;autoencoder, in particular. In the past, methods for networ...
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This article presents a methodology for the Synthesis of PARallel multi-Threaded Accelerators (SPARTA) from OpenMP annotated C/C++ specifications. SPARTA extends an open-source HLS tool, enabling the generation of acc...
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This article presents a methodology for the Synthesis of PARallel multi-Threaded Accelerators (SPARTA) from OpenMP annotated C/C++ specifications. SPARTA extends an open-source HLS tool, enabling the generation of accelerators that provide latency tolerance for irregular memory accesses through multithreading, support fine-grained memory-level parallelism through a hot-potato deflection-based network-on-chip (NoC), support synchronization constructs, and can instantiate memory-side caches. Our approach is based on a custom runtime OpenMP library, providing flexibility and extensibility. Experimental results show high scalability when synthesizing irregular graph kernels. The accelerators generated with our approach are, on average, 2.29x faster than state-of-the-art HLS methodologies.
Picking up multiple objects at once is a grasping skill that makes a human worker efficient in many domains. This work tackles the problem of getting a requested number of identical objects in a shallow bin by only pi...
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