Abstract
We consider the problem of inferring a graph (and a sequence) from the numbers of occurrences of vertex-labeled paths, which is closely related to the pre-image problem for graphs in machine learning: to reconstruct a graph from its feature space representation. We show that this problem can be solved in polynomial time in the size of an output graph if graphs are trees of bounded degree and the lengths of given paths are bounded by a constant. On the other hand, we show that this problem is strongly NP-hard even for planar graphs of bounded degree.
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References
Asano, T.: An O(n log log n) time algorithm for constructing a graph of maximum connectivity with prescribed degrees. J. Computer and System Sciences 51, 503–510 (1995)
Bakir, G.H., Weston, J., Schölkopf, B.: Learning to find pre-images. Advances in Neural Information Processing Systems 16, 449–456 (2004)
Bakir, G.H., Zien, A., Tsuda, K.: Learning to find graph pre-images. In: Rasmussen, C.E., Bülthoff, H.H., Schölkopf, B., Giese, M.A. (eds.) DAGM 2004. LNCS, vol. 3175, pp. 253–261. Springer, Heidelberg (2004)
Cortes, C., Vapnik, V.: Support vector networks. Machine Learning 20, 273–297 (1995)
Cristianini, N., Shawe-Taylor, J.: An Introduction to Support Vector Machines and Other Kernel-based Learning Methods. Cambridge Univ. Press, Cambridge (2000)
Dinitz, Y., Itai, A., Rodeh, M.: On an algorithm of Zemlyachenko for subtree isomorphism. Information Processing Letters 70, 141–146 (1999)
Garey, M.R., Johnson, D.S.: Computers and Intractability. A Guide to the Theory of NP-Completeness. W.H. Freeman and Co., New York (1979)
Kashima, H., Tsuda, K., Inokuchi, A.: Marginalized kernels between labeled graphs. In: Proc. 20th Int. Conf. Machine Learning, pp. 321–328 (2003)
Lauri, J., Scapellato, R.: Topics in Graph Automorphisms and Reconstruction. Cambridge Univ. Press, Cambridge (2003)
Leslie, C., Eskin, E., Noble, W.S.: The spectrum kernel: a string kernel for SVM protein classification. In: Proc. Pacific Symposium on Biocomputing, vol. 7, pp. 564–575 (2002)
Mahé, P., Ueda, N., Akutsu, T., Perret, J.-L., Vert, J.-P.: Extensions of marginalized graph kernels. In: Proc. 21st Int. Conf. Machine Learning, pp. 552–559 (2004)
Maruyama, O., Miyano, S.: Inferring a tree from walks. Theoretical Computer Science 161, 289–300 (1996)
Nachbar, R.B.: Molecular evolution: automated manipulation of hierarchical chemical topology and its application to average molecular structures. Genetic Programming and Evolvable Machines 1, 57–94 (2000)
Pevzner, P.A.: Computational Molecular Biology. An Algorithmic Approach. The MIT Press, Cambridge (2000)
Raghavan, V.: Bounded degree graph inference from walks. J. Computer and System Sciences 49, 108–132 (1994)
Schölkopf, B., Tsuda, K., Vert, J.-P. (eds.): Kernel Methods in Computational Biology. The MIT Press, Cambridge (2004)
Vinkers, H.M., de Jonge, M.R., Daeyaert, F.F.D., Heeres, J., Koymans, L.M.H., van Lenthe, J.H., Lewi, P.J., Timmerman, H., van Aken, K., Janssen, P.A.J.: Synopsis: synthesize and optimize system in silico. Journal of Medical Chemistry 46, 2765–2773 (2003)
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Akutsu, T., Fukagawa, D. (2005). Inferring a Graph from Path Frequency. In: Apostolico, A., Crochemore, M., Park, K. (eds) Combinatorial Pattern Matching. CPM 2005. Lecture Notes in Computer Science, vol 3537. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11496656_32
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DOI: https://doi.org/10.1007/11496656_32
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-26201-5
Online ISBN: 978-3-540-31562-9
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