scholarly journals An experimental evaluation of refinement techniques for the subgraph isomorphism backtracking algorithms

2020 ◽  
Vol 11 (1) ◽  
pp. 33-42
Author(s):  
Jurij Mihelič ◽  
Uroš Čibej
Keyword(s):  
Experimental Evaluation ◽  
Isomorphism Problem ◽  
Subgraph Isomorphism ◽  
Hard Problem ◽  
Practical Algorithms ◽  
Experimental Algorithmics ◽  
Speed Up

AbstractIn this paper, we study a well-known computationally hard problem, called the subgraph isomorphism problem where the goal is for a given pattern and target graphs to determine whether the pattern is a subgraph of the target graph. Numerous algorithms for solving the problem exist in the literature and most of them are based on the backtracking approach. Since straightforward backtracking is usually slow, many algorithmic refinement techniques are used in practical algorithms. The main goal of this paper is to study such refinement techniques and to determine their ability to speed up backtracking algorithms. To do this we use a methodology of experimental algorithmics. We perform an experimental evaluation of the techniques and their combinations and, hence, demonstrate their usefulness in practice.

scholarly journals Diamond Subgraphs in the Reduction Graph of a One-Rule String Rewriting System

2021 ◽  
Vol 178 (3) ◽  
pp. 173-185
Author(s):  
Arthur Adinayev ◽  
Itamar Stein
Keyword(s):  
Isomorphism Problem ◽  
Complete Characterization ◽  
Hasse Diagram ◽  
Subgraph Isomorphism ◽  
Rewriting Systems ◽  
Rewriting System ◽  
String Rewriting ◽  
Reduction Graph

In this paper, we study a certain case of a subgraph isomorphism problem. We consider the Hasse diagram of the lattice Mk (the unique lattice with k + 2 elements and one anti-chain of length k) and find the maximal k for which it is isomorphic to a subgraph of the reduction graph of a given one-rule string rewriting system. We obtain a complete characterization for this problem and show that there is a dichotomy. There are one-rule string rewriting systems for which the maximal such k is 2 and there are cases where there is no maximum. No other intermediate option is possible.

scholarly journals ConnectIt

2020 ◽  
Vol 14 (4) ◽  
pp. 653-667
Author(s):  
Laxman Dhulipala ◽  
Changwan Hong ◽  
Julian Shun
Keyword(s):  
Experimental Evaluation ◽  
Comprehensive Evaluation ◽  
State Of The Art ◽  
Graph Connectivity ◽  
Connected Components ◽  
Sampling Strategies ◽  
Spanning Forest ◽  
Speed Up ◽  
Minimum Spanning Forest ◽  
Edge Sampling

Connected components is a fundamental kernel in graph applications. The fastest existing multicore algorithms for solving graph connectivity are based on some form of edge sampling and/or linking and compressing trees. However, many combinations of these design choices have been left unexplored. In this paper, we design the ConnectIt framework, which provides different sampling strategies as well as various tree linking and compression schemes. ConnectIt enables us to obtain several hundred new variants of connectivity algorithms, most of which extend to computing spanning forest. In addition to static graphs, we also extend ConnectIt to support mixes of insertions and connectivity queries in the concurrent setting. We present an experimental evaluation of ConnectIt on a 72-core machine, which we believe is the most comprehensive evaluation of parallel connectivity algorithms to date. Compared to a collection of state-of-the-art static multicore algorithms, we obtain an average speedup of 12.4x (2.36x average speedup over the fastest existing implementation for each graph). Using ConnectIt, we are able to compute connectivity on the largest publicly-available graph (with over 3.5 billion vertices and 128 billion edges) in under 10 seconds using a 72-core machine, providing a 3.1x speedup over the fastest existing connectivity result for this graph, in any computational setting. For our incremental algorithms, we show that our algorithms can ingest graph updates at up to several billion edges per second. To guide the user in selecting the best variants in ConnectIt for different situations, we provide a detailed analysis of the different strategies. Finally, we show how the techniques in ConnectIt can be used to speed up two important graph applications: approximate minimum spanning forest and SCAN clustering.

scholarly journals A Convex Relaxation Bound for Subgraph Isomorphism

2012 ◽  
Vol 2012 ◽  
pp. 1-18
Author(s):  
Christian Schellewald
Keyword(s):  
Lower Bound ◽  
Structural Information ◽  
Convex Relaxation ◽  
Maximum Clique ◽  
Combinatorial Problem ◽  
Isomorphism Problem ◽  
Maximum Clique Problem ◽  
Subgraph Isomorphism ◽  
Semidefinite Programming Relaxation ◽  
Problem Instances

In this work a convex relaxation of a subgraph isomorphism problem is proposed, which leads to a new lower bound that can provide a proof that a subgraph isomorphism between two graphs can not be found. The bound is based on a semidefinite programming relaxation of a combinatorial optimisation formulation for subgraph isomorphism and is explained in detail. We consider subgraph isomorphism problem instances of simple graphs which means that only the structural information of the two graphs is exploited and other information that might be available (e.g., node positions) is ignored. The bound is based on the fact that a subgraph isomorphism always leads to zero as lowest possible optimal objective value in the combinatorial problem formulation. Therefore, for problem instances with a lower bound that is larger than zero this represents a proof that a subgraph isomorphism can not exist. But note that conversely, a negative lower bound does not imply that a subgraph isomorphism must be present and only indicates that a subgraph isomorphism can not be excluded. In addition, the relation of our approach and the reformulation of the largest common subgraph problem into a maximum clique problem is discussed.

Feature Based Search of 3D Databases

2016 ◽  
Author(s):  
Duncan Paterson ◽  
Johnathan Corney
Keyword(s):  
Model Comparison ◽  
Isomorphism Problem ◽  
Graph Representation ◽  
Subgraph Isomorphism ◽  
Target Feature ◽  
Adjacency Graph ◽  
Retrieval Systems ◽  
Experimental Implementation ◽  
3D Databases ◽  
Feature Based

This paper presents a novel algorithm “Twig Match” for feature based shape retrieval systems. The algorithm exploits recent advances in computational methods for subgraph isomorphism, in order to enable databases containing many thousands of components to be searched in less than a second. A face adjacency graph representation is created from a B-Rep model, allowing model comparison to be treated as a labelled subgraph isomorphism problem. This paper describes an experimental implementation which allows interactive specification of a target “feature”. By selectively including geometric filters, on faces and relations between neighbouring faces, the algorithm can ensure that matching topology is not incorrectly identified as matching geometry, while also offering users the ability to improve the precision of both query and results. Experimental results show that Twig Match accurately retrieves matching and similar sub-parts from collections at speeds suitable for interactive applications.

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