Given a graph with k greater than or equal to 2 different nonnegative weights associated with each edge e and a cost function c: R-k --> R+, consider the problem of finding a minimum-cost edge subset possessing a c...
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Given a graph with k greater than or equal to 2 different nonnegative weights associated with each edge e and a cost function c: R-k --> R+, consider the problem of finding a minimum-cost edge subset possessing a certain property P. We prove that this problem is weakly NP-hard for a wide class of properties P and costs c, including paths, spanning trees, cuts, joins, etc. We suggest a simple approximation algorithm for this problem and find its performance guarantee. (C) 2002 Elsevier Science B.V. All rights reserved.
graph algorithms play a prominent role in several fields of sciences and engineering. Notable among them are graph traversal, finding the connected components of a graph, and computing shortest paths. There are severa...
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graph algorithms play a prominent role in several fields of sciences and engineering. Notable among them are graph traversal, finding the connected components of a graph, and computing shortest paths. There are several efficient implementations of the above problems on a variety of modern multiprocessor architectures. It can be noticed in recent times that the size of the graphs that correspond to real world datasets has been increasing. Parallelism offers only a limited succor to this situation as current parallel architectures have severe short-comings when deployed for most graph algorithms. At the same time, these graphs are also getting very sparse in nature. This calls for particular solution strategies aimed at processing large, sparse graphs on modern parallel architectures. In this paper, we introduce graph pruning as a technique that aims to reduce the size of the graph. Certain elements of the graph can be pruned depending on the nature of the computation. Once a solution is obtained on the pruned graph, the solution is extended to the entire graph. Towards, this end we investigate pruning based on two strategies that justifies their use in current real world graphs. We apply the above technique on three fundamental graph algorithms: breadth first search (BFS), Connected Components (CC), and All Pairs Shortest Paths (APSP). For experimentations, we use three different sources for real world graphs. To validate our technique, we implement our algorithms on a heterogeneous platform consisting of a multicore CPU and a GPU. On this platform, we achieve an average of 35% improvement compared to state-of-the-art solutions. Such an improvement has the potential to speed up other applications reliant on these algorithms. (C) 2014 Elsevier Inc. All rights reserved.
graph cut algorithms are popular in optimization tasks related to min-cut and max-flow problems. However, modern FPGA graph cut algorithm accelerators still need performance and memory resource utilization optimizatio...
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The intensively studied DIAMETER problem is to find the diameter of a given connected graph. We investigate, for the first time in a structured manner, the complexity of DIAMETER for H-free graphs, that is, graphs tha...
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ISBN:
(纸本)9783031754081;9783031754098
The intensively studied DIAMETER problem is to find the diameter of a given connected graph. We investigate, for the first time in a structured manner, the complexity of DIAMETER for H-free graphs, that is, graphs that do not contain a fixed graph H as an induced subgraph. We first show that if H is not a linear forest with small components, then DIAMETER cannot be solved in subquadratic time for H-free graphs under SETH. For some small linear forests, we do show linear-time algorithms for solving DIAMETER. For other linear forests H, we make progress towards linear-time algorithms by considering specific diameter values. If H is a linear forest, the maximum value of the diameter of any graph in a connected H-free graph class is some constant d(max) dependent only on H. We give linear-time algorithms for deciding if a connected H-free graph has diameter d(max), for several linear forests H. In contrast, for one such linear forest H, DIAMETER cannot be solved in subquadratic time for H-free graphs under SETH. Moreover, we even show that, for several other linear forests H, one cannot decide in subquadratic time if a connected H-free graph has diameter d(max) under SETH.
For a graph G in read-only memory on n vertices and m edges and a write-only output buffer, we give two algorithms using only O(n) rewritable space. The first algorithm lists all minimal a - b separators of G with a p...
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For a graph G in read-only memory on n vertices and m edges and a write-only output buffer, we give two algorithms using only O(n) rewritable space. The first algorithm lists all minimal a - b separators of G with a polynomial delay of O(nm). The second lists all minimal vertex separators of G with a cumulative polynomial delay of O(n(3)m). One consequence is that the algorithms can list the minimal a - b separators (and minimal vertex separators) spending O(nm) time (respectively, O(n(3)m) time) per object output. (C) 2010 Elsevier B.V. All rights reserved.
Hop-constrained s-t simple path (HC-s-t path) enumeration is a core problem in graph analysis, commonly applied to unlabelled graphs without considering label constraints. However, in many practical scenarios, graphs ...
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ISBN:
(纸本)9789819612413;9789819612420
Hop-constrained s-t simple path (HC-s-t path) enumeration is a core problem in graph analysis, commonly applied to unlabelled graphs without considering label constraints. However, in many practical scenarios, graphs are edge-labelled, requiring queries to satisfy specific label constraints on the paths between vertices. This introduces new computational challenges that traditional HC-s-t path algorithms are not equipped to handle, especially in distributed environments dealing with large-scale graphs. To address these challenges, we propose a distributed algorithm for labelled hop-constrained s-t path (LHC-s-t path) enumeration. Our approach introduces an online label-based index to prune unnecessary computations, reducing both redundant processing and communication overhead. This enables efficient LHC-s-t path enumeration across distributed systems. Extensive experiments on large real-world graphs demonstrate that our algorithm significantly outperforms existing methods, achieving over an order of magnitude improvement in performance and scalability.
In this paper, we present efficient parallel algorithms for the following graph problems: finding the lowest common ancestors for vertex pairs of a directed tree; finding all fundamental cycles, a directed spanning fo...
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In this paper, we present efficient parallel algorithms for the following graph problems: finding the lowest common ancestors for vertex pairs of a directed tree; finding all fundamental cycles, a directed spanning forest, all bridges, all bridge-connected components, all separation vertices, all biconnected components, and testing the biconnectivity of an undirected graph. All these algorithms achieve the $O(\lg ^2 n)$ time bound, with the first two algorithms using $n\lceil n /\lg n\rceil $ processors and the remaining algorithms using $n\lceil n/\lg ^2 n \rceil $ processors. In all cases, our algorithms are better than the previously known algorithms and in most cases reduce the number of processors used by a factor of $n\lg n$. Moreover, our algorithms are optimal with respect to the time-processor product for dense graphs, with the exception of the first two algorithms.
For a given graph G, a maximum internal spanning tree of G is a spanning tree of G with maximum number of internal vertices. The Maximum Internal Spanning Tree (MIST) problem is to find a maximum internal spanning tre...
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For a given graph G, a maximum internal spanning tree of G is a spanning tree of G with maximum number of internal vertices. The Maximum Internal Spanning Tree (MIST) problem is to find a maximum internal spanning tree of the given graph. The MIST problem is a generalization of the Hamiltonian path problem. Since the Hamiltonian path problem is NP-hard, even for bipartite and chordal graphs, two important subclasses of graphs, the MIST problem also remains NP-hard for these graph classes. In this paper, we propose linear-time algorithms to compute a maximum internal spanning tree of cographs, block graphs, cactus graphs, chain graphs and bipartite permutation graphs. The optimal path cover problem, which asks to find a path cover of the given graph with maximum number of edges, is also a well studied problem. In this paper, we also study the relationship between the number of internal vertices in maximum internal spanning tree and number of edges in optimal path cover for the special graph classes mentioned above.
Triangle counting is a fundamental graph algorithm used to identify the number of triangles within a graph. This algorithm can be reformulated into linear algebraic operations, including sparse matrix multiplication, ...
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ISBN:
(纸本)9798400714436
Triangle counting is a fundamental graph algorithm used to identify the number of triangles within a graph. This algorithm can be reformulated into linear algebraic operations, including sparse matrix multiplication, intersection and reduction. Modern GPUs, equipped with Tensor Cores, offer massive parallelism that can significantly accelerate graph algorithms. However, leveraging Tensor Cores, originally designed for dense matrix multiplication, to handle sparse workloads for triangle counting presents non-trivial challenges. In this paper, we introduce ToT, which enhances the utilization of Tensor Cores and expands their functionalities for diverse sparse matrix operations. In experiments, ToT is evaluated against state-of-the-art methods. ToT outperform the second-fastest method with an 11.56x speedup in end-to-end execution. This work represents a pioneering exploration into utilizing Tensor Cores for accelerating graph algorithms.
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