scholarly journals SEARCH-TREE SIZE ESTIMATION FOR THE SUBGRAPH ISOMORPHISM PROBLEM

2018 ◽  
Vol 18 (4) ◽  
pp. 3-10
Author(s):  
Uroš Čibej ◽  
◽  
Jurij Mihelič
Keyword(s):  
Isomorphism Problem ◽  
Search Tree ◽  
Tree Size ◽  
Subgraph Isomorphism ◽  
Size Estimation

scholarly journals A Learning Based Branch and Bound for Maximum Common Subgraph Related Problems

2020 ◽  
Vol 34 (03) ◽  
pp. 2392-2399
Author(s):  
Yanli Liu ◽  
Chu-Min Li ◽  
Hua Jiang ◽  
Kun He
Keyword(s):  
Reinforcement Learning ◽  
Branch And Bound ◽  
Search Tree ◽  
Tree Size ◽  
Experimental Results ◽  
Subgraph Isomorphism ◽  
Connected Subgraph ◽  
Induced Subgraph ◽  
Maximum Common Subgraph ◽  
Tree Leaf

The performance of a branch-and-bound (BnB) algorithm for maximum common subgraph (MCS) problem and its related problems, like maximum common connected subgraph (MCCS) and induced Subgraph Isomorphism (SI), crucially depends on the branching heuristic. We propose a branching heuristic inspired from reinforcement learning with a goal of reaching a tree leaf as early as possible to greatly reduce the search tree size. Experimental results show that the proposed heuristic consistently and significantly improves the current best BnB algorithm for the MCS, MCCS and SI problems. An analysis is carried out to give insight on why and how reinforcement learning is useful in the new branching heuristic.

scholarly journals Clairvoyant Restarts in Branch-and-Bound Search Using Online Tree-Size Estimation

2019 ◽  
Vol 33 ◽  
pp. 1427-1434 ◽  
Author(s):  
Daniel Anderson ◽  
Gregor Hendel ◽  
Pierre Le Bodic ◽  
Merlin Viernickel
Keyword(s):  
Branch And Bound ◽  
State Of The Art ◽  
Search Tree ◽  
Tree Size ◽  
Large Set ◽  
Size Estimation ◽  
Current Estimate ◽  
Benchmark Instances ◽  
Branch And Bound Search ◽  
Restart Strategy

We propose a simple and general online method to measure the search progress within the Branch-and-Bound algorithm, from which we estimate the size of the remaining search tree. We then show how this information can help solvers algorithmically at runtime by designing a restart strategy for MixedInteger Programming (MIP) solvers that decides whether to restart the search based on the current estimate of the number of remaining nodes in the tree. We refer to this type of algorithm as clairvoyant. Our clairvoyant restart strategy outperforms a state-of-the-art solver on a large set of publicly available MIP benchmark instances. It is implemented in the MIP solver SCIP and will be available in future releases.

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 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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