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alpar@0: %% Template article for Elsevier's document class `elsarticle'
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alpar@1: \journal{Discrete Applied Mathematics}
alpar@0: 
alpar@0: \begin{document}
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alpar@0: \begin{frontmatter}
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alpar@0: %% Title, authors and addresses
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alpar@1: \title{Improved Algorithms for Matching Biological Graphs}
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alpar@0: 
alpar@1: \author{Alp{\'a}r J{\"u}ttner and P{\'e}ter Madarasi}
alpar@0: 
alpar@1: \address{Dept of Operations Research, ELTE}
alpar@0: 
alpar@0: \begin{abstract}
alpar@1: Subgraph isomorphism is a well-known NP-Complete problem, while its
alpar@1: special case, the graph isomorphism problem is one of the few problems
alpar@1: in NP neither known to be in P nor NP-Complete. Their appearance in
alpar@1: many fields of application such as pattern analysis, computer vision
alpar@1: questions and the analysis of chemical and biological systems has
alpar@1: fostered the design of various algorithms for handling special graph
alpar@1: structures.
alpar@0: 
alpar@1: The idea of using state space representation and checking some
alpar@1: conditions in each state to prune the search tree has made the VF2
alpar@1: algorithm one of the state of the art graph matching algorithms for
alpar@1: more than a decade. Recently, biological questions of ever increasing
alpar@1: importance have required more efficient, specialized algorithms.
alpar@1: 
alpar@1: This paper presents VF2++, a new algorithm based on the original VF2,
alpar@1: which runs significantly faster on most test cases and performs
alpar@1: especially well on special graph classes stemming from biological
alpar@1: questions. VF2++ handles graphs of thousands of nodes in practically
alpar@1: near linear time including preprocessing. Not only is it an improved
alpar@1: version of VF2, but in fact, it is by far the fastest existing
alpar@1: algorithm regarding biological graphs.
alpar@1: 
alpar@1: The reason for VF2++' superiority over VF2 is twofold. Firstly, taking
alpar@1: into account the structure and the node labeling of the graph, VF2++
alpar@1: determines a state order in which most of the unfruitful branches of
alpar@1: the search space can be pruned immediately. Secondly, introducing more
alpar@1: efficient - nevertheless still easier to compute - cutting rules
alpar@1: reduces the chance of going astray even further.
alpar@1: 
alpar@1: In addition to the usual subgraph isomorphism, specialized versions
alpar@1: for induced subgraph isomorphism and for graph isomorphism are
alpar@1: presented. VF2++ has gained a runtime improvement of one order of
alpar@1: magnitude respecting induced subgraph isomorphism and a better
alpar@1: asymptotical behaviour in the case of graph isomorphism problem.
alpar@1: 
alpar@1: After having provided the description of VF2++, in order to evaluate
alpar@1: its effectiveness, an extensive comparison to the contemporary other
alpar@1: algorithms is shown, using a wide range of inputs, including both real
alpar@1: life biological and chemical datasets and standard randomly generated
alpar@1: graph series.
alpar@1: 
alpar@1: The work was motivated and sponsored by QuantumBio Inc., and all the
alpar@1: developed algorithms are available as the part of the open source
alpar@1: LEMON graph and network optimization library
alpar@1: (http://lemon.cs.elte.hu).
alpar@0: \end{abstract}
alpar@0: 
alpar@0: \begin{keyword}
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alpar@0: \end{keyword}
alpar@0: 
alpar@0: \end{frontmatter}
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