Abstract
Graph orientation is a fundamental problem in graph theory that has recently arisen in the study of signaling-regulatory pathways in protein networks. Given a graph and a list of ordered source-target vertex pairs, it calls for assigning directions to the edges of the graph so as to maximize the number of pairs that admit a directed source-to-target path. When the input graph is undirected, a sub-logarithmic approximation is known for the problem. However, the approximability of the biologically-relevant variant, in which the input graph has both directed and undirected edges, was left open. Here we give the first approximation algorithm to this problem. Our algorithm provides a sub-linear guarantee in the general case, and logarithmic guarantees for structured instances.
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References
Arkin, E.M., Hassin, R.: A note on orientations of mixed graphs. Discrete Applied Mathematics 116(3), 271–278 (2002)
Bafna, V., Berman, P., Fujito, T.: A 2-approximation algorithm for the undirected feedback vertex set problem. SIAM Journal on Discrete Mathematics 12(3), 289–297 (1999)
Bang-Jensen, J., Gutin, G.: Digraphs: Theory, Algorithms and Applications, 2nd edn. Springer, Heidelberg (2008)
Barabási, A.-L., Oltvai, Z.N.: Network biology: understanding the cell’s functional organization. Nature Reviews Genetics 5(2), 101–113 (2004)
Boesch, F., Tindell, R.: Robbins’s theorem for mixed multigraphs. The American Mathematical Monthly 87(9), 716–719 (1980)
Chen, J., Fomin, F.V., Liu, Y., Lu, S., Villanger, Y.: Improved algorithms for feedback vertex set problems. Journal of Computer and System Sciences 74(7), 1188–1198 (2008)
Chung, F.R.K., Garey, M.R., Tarjan, R.E.: Strongly connected orientations of mixed multigraphs. Networks 15(4), 477–484 (1985)
Cohen, R., Havlin, S., ben-Avraham, D.: Structural properties of scale-free networks. In: Handbook of Graphs and Networks: From the Genome to the Internet. Wiley-VCH, Weinheim (2002)
Dorn, B., Hüffner, F., Krüger, D., Niedermeier, R., Uhlmann, J.: Exploiting bounded signal flow for graph orientation based on cause–effect pairs (To appear). In: Marchetti-Spaccamela, A., Segal, M. (eds.) TAPAS 2011. LNCS, vol. 6595, pp. 104–115. Springer, Heidelberg (2011)
Fields, S.: High-throughput two-hybrid analysis. The promise and the peril. The FEB Journal 272(21), 5391–5399 (2005)
Flum, J., Grohe, M.: Parameterized Complexity Theory. Springer, Heidelberg (2006)
Frederickson, G.N., Johnson, D.B.: Generating and searching sets induced by networks. In: ICALP 1980. LNCS, vol. 85, pp. 221–233. Springer, Heidelberg (1980)
Gamzu, I., Segev, D., Sharan, R.: Improved orientations of physical networks. In: Moulton, V., Singh, M. (eds.) WABI 2010. LNCS, vol. 6293, pp. 215–225. Springer, Heidelberg (2010)
Gavin, A., Bösche, M., Krause, R., Grandi, P., Marzioch, M., Bauer, A., Schultz, J., Rick, J.M., Michon, A.-M., Cruciat, C.-M., Remor, M., Höfert, C., Schelder, M., Brajenovic, M., Ruffner, H., Merino, A., Klein, K., Hudak, M., Dickson, D., Rudi, T., Gnau, V., Bauch, A., Bastuck, S., Huhse, B., Leutwein, C., Heurtier, M.-A., Copley, R.R., Edelmann, A., Querfurth, E., Rybin, V., Drewes, G., Raida, M., Bouwmeester, T., Bork, P., Seraphin, B., Kuster, B., Neubauer, G., Superti-Furga, G.: Functional organization of the yeast proteome by systematic analysis of protein complexes. Nature 415(6868), 141–147 (2002)
Hakimi, S.L., Schmeichel, E.F., Young, N.E.: Orienting graphs to optimize reachability. Information Processing Letters 63(5), 229–235 (1997)
Håstad, J.: Some optimal inapproximability results. Journal of the ACM 48(4), 798–859 (2001)
Karp, R.M.: Reducibility among combinatorial problems. In: Complexity of Computer Computations, pp. 85–103. Plenum Press, New York (1972)
Medvedovsky, A., Bafna, V., Zwick, U., Sharan, R.: An algorithm for orienting graphs based on cause-effect pairs and its applications to orienting protein networks. In: Crandall, K.A., Lagergren, J. (eds.) WABI 2008. LNCS (LNBI), vol. 5251, pp. 222–232. Springer, Heidelberg (2008)
Newman, M.E.J.: The structure and function of complex networks. SIAM Review 45(2), 167–256 (2003)
Robbins, H.E.: A theorem on graphs, with an application to a problem of traffic control. The American Mathematical Monthly 46(5), 281–283 (1939)
Silverbush, D., Elberfeld, M., Sharan, R.: Optimally orienting physical networks. In: Bafna, V., Sahinalp, S.C. (eds.) RECOMB 2011. LNCS, vol. 6577, pp. 424–436. Springer, Heidelberg (2011)
Tarjan, R.E.: A note on finding the bridges of a graph. Information Processing Letters 2(6), 160–161 (1974)
Yeang, C., Ideker, T., Jaakkola, T.: Physical network models. Journal of Computational Biology 11(2-3), 243–262 (2004)
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Elberfeld, M., Segev, D., Davidson, C.R., Silverbush, D., Sharan, R. (2011). Approximation Algorithms for Orienting Mixed Graphs. In: Giancarlo, R., Manzini, G. (eds) Combinatorial Pattern Matching. CPM 2011. Lecture Notes in Computer Science, vol 6661. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-21458-5_35
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DOI: https://doi.org/10.1007/978-3-642-21458-5_35
Publisher Name: Springer, Berlin, Heidelberg
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