This paper analyzes a blockchain network forming a directed acyclic graph (DAG), called a DAG-type blockchain, from the view-point of graph algorithm theory. To use a DAG-type blockchain, NP-hard graph optimization pr...
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This paper analyzes a blockchain network forming a directed acyclic graph (DAG), called a DAG-type blockchain, from the view-point of graph algorithm theory. To use a DAG-type blockchain, NP-hard graph optimization problems on the DAG are required to be solved. Although various problems for undirected and directed graphs can be efficiently solved by using the notions of graph parameters, these currently known parameters are meaningless for DAGs, which implies that it is hopeless to design efficient algorithms based on the parameters for such problems. In this work, we propose a novel graph parameter for directed graphs called a DAG-pathwidth, which represents the closeness to a directed path. This is an extension of the pathwidth, a well-known graph parameter for undirected graphs. We analyze the features of the DAG-pathwidth and prove that computing the DAG-pathwidth of a DAG (directed graph in general) is NP-complete. Finally, we propose an efficient algorithm for a variant of the maximum k-independent set problem for the DAG-type blockchain when the DAG-pathwidth of the input graph is small.
Although there are polynomial algorithms of finding a 2-partition or a 3-partition for a simple undirected 2-connected or 3-connected graph respectively, there is no general algorithm of finding a k-partition for a k-...
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Although there are polynomial algorithms of finding a 2-partition or a 3-partition for a simple undirected 2-connected or 3-connected graph respectively, there is no general algorithm of finding a k-partition for a k-connected graph G = (V, E), where k is the vertex connectivity of G. In this paper, an O(k2n2) general algorithm of finding a k-partition for a k-connected graph is proposed, where n = |V|.
Matrix multiplication algorithms for cube connected and perfect shuffle computers are presented. It is shown that in both these models two n×nn×nn \times n matrices can be multiplied in <span class="...
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Implementing non-trivial algorithms, like many graph algorithms, is generally expensive, Thus, it is desirable to reuse such implementations whenever possible. The implementations of graph algorithms normally cannot b...
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ISBN:
(纸本)3540410902
Implementing non-trivial algorithms, like many graph algorithms, is generally expensive, Thus, it is desirable to reuse such implementations whenever possible. The implementations of graph algorithms normally cannot be reused mainly because the representations of graphs differ in many ways and the implementations normally assume one specific representation. This article presents an approach to overcoming this problem which is based mainly on special iterators and special means to access data associated with objects.
graph algorithms are notorious for not getting good speedup on parallel architectures. These algorithms tend to suffer from irregular dependencies and a high synchronization cost that prevent an efficient execution on...
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ISBN:
(纸本)9780769546766
graph algorithms are notorious for not getting good speedup on parallel architectures. These algorithms tend to suffer from irregular dependencies and a high synchronization cost that prevent an efficient execution on distributed memory machines. Hence such algorithms are mostly parallelized on shared memory machines. However, current commodity shared memory machines do not typically offer enough parallelism to process these problems. In this paper, we are presenting an early investigation of the scalability of such algorithms on Intel's upcoming Many Integrated Core (Intel MIC) architecture which, when it will be released in 2012, is expected to provide more than 50 physical cores with SMT capability. The Intel MIC architecture can be programmed through many programming models, here we investigate the three most popular of these models namely OpenMP, Cilk Plus and Intel's TBB. We present scalability results of a parallel graph coloring algorithm, three variations of a breadth-first search algorithm and a microbenchmark for irregular computations using these three programming models. Our results on a prototype board show that the multi-threaded architecture of Intel MIC can be effectively used for hiding latencies in irregular applications to achieve almost perfect speedup.
The task of the Wind Farm Cable Layout Problem is to design a cable system between turbines and substations such that all turbine output can be transmitted to the substations. This problem can be modelled with differe...
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ISBN:
(纸本)9781665443890
The task of the Wind Farm Cable Layout Problem is to design a cable system between turbines and substations such that all turbine output can be transmitted to the substations. This problem can be modelled with different levels of complexity. While a higher level of complexity yields solutions that can be implemented in a real-world setting more readily, problem instances also become more difficult to solve or even remain intractable. More simplistic models are easier to solve but their usability could be inhibited. One such more simplistic model for installation cost minimization contains a network flow and a suitable minimum-cost flow algorithm provides good cable layouts on instances with up to 500 turbines within tens of seconds. The question remains whether those cable layouts are suitable for electrical implementation as well. We propose a workflow to evaluate the cable layouts generated from such algorithms under electrical aspects. This workflow converts the output of cable layout optimization algorithms to power flow models. The power flow models are simulated using the simulation framework eASiMOV. The evaluation of the power flow simulations under electrical metrics shows that output from the minimum-cost flow algorithm and from an approach solving a Mixed-Integer Linear Program perform very well under electrical aspects on a vast majority of input instances. For the remaining minority we are able to identify structures in the solutions that result in a worse performance. These observations can be used by the algorithm engineers as possible directions for future improvements.
Community detection is a cornerstone problem in social network analysis (SNA), aimed at identifying cohesive communities with minimal external links. However, the rise of generative AI and Metaverse introduce complexi...
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In this article, we consider the following problem. Given a directed graph G, output all walks of G that are sub-walks of all closed edge-covering walks of G. This problem was first considered by Tomescu and Medvedev ...
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In this article, we consider the following problem. Given a directed graph G, output all walks of G that are sub-walks of all closed edge-covering walks of G. This problem was first considered by Tomescu and Medvedev (RECOMB 2016), who characterized these walks through the notion of omnitig. Omnitigs were shown to be relevant for the genome assembly problem from bioinformatics, where a genome sequence must be assembled from a set of reads from a sequencing experiment. Tomescu and Medvedev (RECOMB 2016) also proposed an algorithm for listing all maximal omnitigs, by launching an exhaustive visit from every edge. In this article, we prove new insights about the structure of omnitigs and solve several open questions about them. We combine these to achieve an O(nm)-time algorithm for outputting all the maximal omnitigs of a graph (with n nodes and m edges). This is also optimal, as we show families of graphs whose total omnitig length is Omega(nm). We implement this algorithm arid show that it is 9-12 times faster in practice than the one of Tomescu and Medvedev (RECOMB 2016).
How do we develop programs that are easy to express, easy to reason about, and able to achieve high performance on massively parallel machines? To address this problem, we introduce graph Step, a domain-specific compu...
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How do we develop programs that are easy to express, easy to reason about, and able to achieve high performance on massively parallel machines? To address this problem, we introduce graph Step, a domain-specific compute model that captures algorithms that act on static, irregular, sparse graphs. In graph Step, algorithms are expressed directly without requiring the programmer to explicitly manage parallel synchronization, operation ordering, placement, or scheduling details. Problems in the sparse graph domain are usually highly concurrent and communicate along graph edges. Exposing concurrency and communication structure allows scheduling of parallel operations and management of communication that is necessary for performance on a spatial computer. We study the performance of a semantic network application, a shortest-path application, and a max-flow/min-cut application. We introduce a language syntax for graphStep applications. The total speedup over sequential versions of the applications studied ranges from a factor of 19 to a factor of 15,000. Spatially-aware graph optimizations (e.g., node decomposition, placement and route scheduling) delivered speedups from 3 to 30 times over a spatially-oblivious mapping.
Two graph algorithms which derive from bread-first search were implemented by using C language in this paper. One algorithm is a replacement method for finding out a graph's all spanning tree, the other is the Pat...
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Two graph algorithms which derive from bread-first search were implemented by using C language in this paper. One algorithm is a replacement method for finding out a graph's all spanning tree, the other is the Paton algorithm for finding out all essential circuit of a graph. This paper mainly introduced the flow of the two graph algorithms. An illustrative example was presented. Also, a practical operational platform of graph algorithm was designed and realized in this paper.
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