We present an exact partial enumerative algorithm for the maximum clique problem. The pruning device used is derived from graph colorings. Pruning of the search tree is accomplished not only by the number of colors used to color a tree subproblem but also by using information gained in the process of coloring. This leads to increased pruning which translates into improved computational performance. Experimental results on test problems are presented.

An exact algorithm for the maximum clique problem with accelerated pruning

https://hal.univ-angers.fr/hal-02709508/document

A review on algorithms for maximum clique problems

Variable neighborhood search for the maximum clique

This paper formalises the idea of substitutability introduced by Zellig Harris in the 1950s and makes it the basis for a learning algorithm from positive data only for a subclass of context-free languages. We show that there is a polynomial characteristic set, and thus prove polynomial identification in the limit of this class. We discuss the relationship of this class of languages to other common classes discussed in grammatical inference. It transpires that it is not necessary to identify constituents in order to learn a context-free language—it is sufficient to identify the syntactic congruence, and the operations of the syntactic monoid can be converted into a context-free grammar. We also discuss modifications to the algorithm that produces a reduction system rather than a context-free grammar, that will be much more compact. We discuss the relationship to Angluin's notion of reversibility for regular languages. We also demonstrate that an implementation of this algorithm is capable of learning a classic example of structure dependent syntax in English: this constitutes a refutation of an argument that has been used in support of nativist theories of language.

/pdf/polynomial-identification-in-the-limit-of-substitutable-8yxvscm48q.pdf

Polynomial Identification in the Limit of Substitutable Context-free Languages

Branch-and-reduce exponential/FPT algorithms in practice

This paper proposes new approximate coloring and other related techniques which markedly improve the run time of the branch-and-bound algorithm MCR (J. Global Optim., 37, 95–111, 2007), previously shown to be the fastest maximum-clique-finding algorithm for a large number of graphs. The algorithm obtained by introducing these new techniques in MCR is named MCS. It is shown that MCS is successful in reducing the search space quite efficiently with low overhead. Consequently, it is shown by extensive computational experiments that MCS is remarkably faster than MCR and other existing algorithms. It is faster than the other algorithms by an order of magnitude for several graphs. In particular, it is faster than MCR for difficult graphs of very high density and for very large and sparse graphs, even though MCS is not designed for any particular type of graphs. MCS can be faster than MCR by a factor of more than 100,000 for some extremely dense random graphs.

A simple and faster branch-and-bound algorithm for finding a maximum clique

We present improvements to a branch-and-bound maximum-clique-finding algorithm MCS (WALCOM 2010, LNCS 5942, pp. 191–203) that was shown to be fast. First, we employ an efficient approximation algorithm for finding a maximum clique. Second, we make use of appropriate sorting of vertices only near the root of the search tree. Third, we employ a lightened approximate coloring mainly near the leaves of the search tree. A new algorithm obtained from MCS with the above improvements is named MCT. It is shown that MCT is much faster than MCS by extensive computational experiments. In particular, MCT is shown to be faster than MCS for gen400_p0.9_75 and gen400_p0.9_65 by over 328,000 and 77,000 times, respectively.

A Much Faster Branch-and-Bound Algorithm for Finding a Maximum Clique

SUMMARY Many problems can be formulated as maximum clique problems. Hence, it is highly important to develop algorithms that can find a maximum clique very fast in practice. We propose new approximate coloring and other related techniques which markedly improve the run time of the branch-and-bound algorithm MCR (J. Global Optim., 37, pp.95–111, 2007), previously shown to be the fastest maximum-clique-finding algorithm for a large number of graphs. The algorithm obtained by introducing these new techniques in MCR is named MCS. It is shown that MCS is successful in reducing the search space quite efficiently with low overhead. Extensive computational experiments confirm the superiority of MCS over MCR and other existing algorithms. It is faster than the other algorithms by orders of magnitude for several graphs. In particular, it is faster than MCR for difficult graphs of very high density and for very large and sparse graphs, even though MCS is not designed for any particular type of graph. MCS can be faster than MCR by a factor of more than 100,000 for some extremely dense random graphs. This paper demonstrates in detail the effectiveness of each new techniques in MCS, as well as the overall contribution.

http://ir.lib.uec.ac.jp/infolib/user_contents/9090000347/9090000347.pdf

A Simple and Faster Branch-and-Bound Algorithm for Finding a Maximum Clique with Computational Experiments

Learning to program is an important subject in computer science courses. During programming exercises, plagiarism by copying and pasting can lead to problems for fair evaluation. Some methods of plagiarism detection are currently available, such as sim. However, because sim is easily influenced by changing the identifier or program statement order, it fails to do enough to support plagiarism detection. In this paper, we propose a plagiarism detection method which is not influenced by changing the identifier or program statement order. We also explain our method's capabilities by comparing it to the sim plagiarism detector. Furthermore, we reveal how our method successfully detects the presence of plagiarism.

Mitsuo Wakatsuki

Papers

A simple and faster branch-and-bound algorithm for finding a maximum clique

A Much Faster Branch-and-Bound Algorithm for Finding a Maximum Clique

A Simple and Faster Branch-and-Bound Algorithm for Finding a Maximum Clique with Computational Experiments

A source code plagiarism detecting method using alignment with abstract syntax tree elements

A Fast Algorithm for Checking the Inclusion for Very Simple Deterministic Pushdown Automata