Topic
Maximum common subgraph isomorphism problem
About: Maximum common subgraph isomorphism problem is a research topic. Over the lifetime, 469 publications have been published within this topic receiving 14252 citations.
Papers published on a yearly basis
Papers
TL;DR: A new algorithm is introduced that attains efficiency by inferentially eliminating successor nodes in the tree search by means of a brute-force tree-search enumeration procedure and a parallel asynchronous logic-in-memory implementation of a vital part of the algorithm is described.
Abstract: Subgraph isomorphism can be determined by means of a brute-force tree-search enumeration procedure. In this paper a new algorithm is introduced that attains efficiency by inferentially eliminating successor nodes in the tree search. To assess the time actually taken by the new algorithm, subgraph isomorphism, clique detection, graph isomorphism, and directed graph isomorphism experiments have been carried out with random and with various nonrandom graphs. A parallel asynchronous logic-in-memory implementation of a vital part of the algorithm is also described, although this hardware has not actually been built. The hardware implementation would allow very rapid determination of isomorphism.
2,520 citations
TL;DR: A survey of results concerning algorithms, complexity, and applications of the maximum clique problem is presented and enumerative and exact algorithms, heuristics, and a variety of other proposed methods are discussed.
Abstract: The maximum clique problem is a classical problem in combinatorial optimization which finds important applications in different domains. In this paper we try to give a survey of results concerning algorithms, complexity, and applications of this problem, and also provide an updated bibliography. Of course, we build upon precursory works with similar goals [39, 232, 266].
1,175 citations
TL;DR: This mapping problem is formulated in graph theoretic terms and shown to be equivalent, in its most general form, to the graph isomorphism problem.
Abstract: In array processors it is important to map problem modules onto processors such that modules that communicate with each other lie, as far as possible, on adjacent processors. This mapping problem is formulated in graph theoretic terms and shown to be equivalent, in its most general form, to the graph isomorphism problem. The problem is also very similar to the bandwidth reduction problem for sparse matrices and to the quadratic assignment problem.
682 citations
TL;DR: A classification and a review of the many MCS algorithms, both exact and approximate, that have been described in the literature, and recommendations regarding their applicability to typical chemoinformatics tasks are made.
Abstract: The maximum common subgraph (MCS) problem has become increasingly important in those aspects of chemoinformatics that involve the matching of 2D or 3D chemical structures. This paper provides a classification and a review of the many MCS algorithms, both exact and approximate, that have been described in the literature, and makes recommendations regarding their applicability to typical chemoinformatics tasks.
495 citations
1 Jan 1993
TL;DR: A highlight of the conference was the presentation of a new quasi-polynomial time algorithm for the Graph Isomorphism Problem, providing the first improvement since 1983.
Abstract: This report documents the program and the outcomes of Dagstuhl Seminar 15511 “The Graph Isomorphism Problem”. The goal of the seminar was to bring together researchers working on the numerous topics closely related to the Isomorphism Problem to foster their collaboration. To this end the participants of the seminar included researchers working on the theoretical and practical aspects of isomorphism ranging from the fields of algorithmic group theory, finite model theory, combinatorial optimization to algorithmics. A highlight of the conference was the presentation of a new quasi-polynomial time algorithm for the Graph Isomorphism Problem, providing the first improvement since 1983. Seminar December 13–18, 2015 – http://www.dagstuhl.de/15511 1998 ACM Subject Classification F.2.2 Nonnumerical Algorithms and Problems, G.2.1 Combinatorics, G.2.2 Graph Theory
381 citations
Related Topics (5)
Performance Metrics
| Year | Papers |
|---|---|
| 2021 | 1 |
| 2020 | 1 |
| 2019 | 1 |
| 2018 | 7 |
| 2017 | 28 |
| 2016 | 22 |