Improvements to Ullmann's Algorithm for the Subgraph Isomorphism Problem

Cibej, Uros; Mihelič, Jurij

doi:10.1142/s0218001415500251

Cited by 18 publications

(7 citation statements)

References 26 publications

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“…The presented algorithm uses the search for subgraphs extensively. Even though, in theory, this is a computationally intractable problem, many practical approaches exist [5,6]. These algorithms work well also on large instances of graphs, especially when pattern graphs are small.…”

Section: Graphlet Based Compressionmentioning

confidence: 99%

Graph automorphisms for compression

Cibej

Mihelič

2020

Open Computer Science

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Detecting automorphisms is a natural way to identify redundant information presented in structured data. When such redundancies are detected they can be used for data compression. In this paper we explore two different classes of graphs to capture this intuitive property of automorphisms. Symmetry-compressible graphs are the first class which introduces the basic concepts but use only global symmetries for the compression. In order for this concept to be more practical, we need to use local symmetries. Thus, we extend the basic graph class with Near Symmetry compressible graphs. Furthermore, we develop two algorithms that can be used to compress practical instances and empirically evaluate them on a set of realistic graphs.

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Section: Graphlet Based Compressionmentioning

confidence: 99%

Graph automorphisms for compression

Cibej

Mihelič

2020

Open Computer Science

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“…Because computers got much faster, and the applications started to deal with more data organized as graphs, the interest for this problem has been increasing, especially in the pattern matching community. New and improved algorithms have started to emerge [7,11,17,19], showing remarkable results on larger and larger instances.…”

Section: Algorithmsmentioning

confidence: 99%

Search-Tree Size Estimation for the Subgraph Isomorphism Problem

Cibej¹,

Mihelič²

2018

AEI

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This article addresses the problem of finding patterns in graphs. This is formally defined as the subgraph isomorphism problem and is one of the core problems in theoretical computer science. We consider the counting variation of this problem. The task is to count all instances of the pattern G occurring in a (usually larger) graph H. The vast majority of algorithms for this problem use a variation of backtracking. Most commonly they exhaustively search through the space of all possible monomorphisms between G and H. The size of the search tree depends heavily on the choice of the ordering of vertices of G, which are systematically assigned to the vertices of H. We use a method called heuristic sampling to estimate the size of the search tree for each ordering in advance. We use this estimation to select the most suitable order of vertices of G which minimizes the expected tree size. This approach is empirically evaluated on a set of instances, showing the practical potential of the method.

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“…The most widely used and well-known practical subgraph isomorphism algorithms are Ullmann's algorithm [8,9], VF variants [10][11][12], RI [13], Glasgow subgraph solver [14], FocusSearch [15], and LAD [16]. The techniques pre-sented in this paper mostly originate from the study of these algorithms.…”

Section: Introductionmentioning

confidence: 99%

“…Moreover, we also have to store the inverse of the mapping function to efficiently obtain a vertex in the pattern which was mapped to a particular target vertex. See also [8] for details.…”

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confidence: 99%

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

Mihelič

Cibej

2020

Open Computer Science

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In 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.

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Improvements to Ullmann's Algorithm for the Subgraph Isomorphism Problem

Cited by 18 publications

References 26 publications

Graph automorphisms for compression

Graph automorphisms for compression

Search-Tree Size Estimation for the Subgraph Isomorphism Problem

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

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