3 results
Domination problems on P5-free graphs∗
- Min Chih Lin, Michel J. Mizrahi
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- Journal:
- RAIRO - Theoretical Informatics and Applications / Volume 48 / Issue 5 / December 2014
- Published online by Cambridge University Press:
- 12 January 2015, pp. 541-549
- Print publication:
- December 2014
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The minimum roman dominating problem (denoted by γR(G), the weight of minimum roman dominating function of graph G) is a variant of the very well known minimum dominating set problem (denoted by γ(G), the cardinality of minimum dominating set of graph G). Both problems remain NP-Complete when restricted to P5-free graph class [A.A. Bertossi, Inf. Process. Lett. 19 (1984) 37–40; E.J. Cockayne, et al. Discret. Math. 278 (2004) 11–22]. In this paper we study both problems restricted to some subclasses of P5-free graphs. We describe robust algorithms that solve both problems restricted to (P5,(s,t)-net)-free graphs in polynomial time. This result generalizes previous works for both problems, and improves existing algorithms when restricted to certain families such as (P5,bull)-free graphs. It turns out that the same approach also serves to solve problems for general graphs in polynomial time whenever γ(G) and γR(G) are fixed (more efficiently than naive algorithms). Moreover, the algorithms described are extremely simple which makes them useful for practical purposes, and as we show in the last section it allows to simplify algorithms for significant classes such as cographs.
Contributors
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- By Jane E. Adcock, Yahya Aghakhani, A. Anand, Eva Andermann, Frederick Andermann, Alexis Arzimanoglou, Sandrine Aubert, Nadia Bahi-Buisson, Carman Barba, Agatino Battaglia, Geneviève Bernard, Nadir E. Bharucha, Laurence A. Bindoff, William Bingaman, Francesca Bisulli, Thomas P. Bleck, Stewart G. Boyd, Andreas Brunklaus, Harry Bulstrode, Jorge G. Burneo, Laura Canafoglia, Laura Cantonetti, Roberto H. Caraballo, Fernando Cendes, Kevin E. Chapman, Patrick Chauvel, Richard F. M. Chin, H. T. Chong, Fahmida A. Chowdhury, Catherine J. Chu-Shore, Rolando Cimaz, Andrew J. Cole, Bernard Dan, Geoffrey Dean, Alessio De Ciantis, Fernando De Paolis, Rolando F. Del Maestro, Irissa M. Devine, Carlo Di Bonaventura, Concezio Di Rocco, Henry B. Dinsdale, Maria Alice Donati, François Dubeau, Michael Duchowny, Olivier Dulac, Monika Eisermann, Brent Elliott, Bernt A. Engelsen, Kevin Farrell, Natalio Fejerman, Rosalie E. Ferner, Silvana Franceschetti, Robert Friedlander, Antonio Gambardella, Hector H. Garcia, Serena Gasperini, Lorenzo Genitori, Gioia Gioi, Flavio Giordano, Leif Gjerstad, Daniel G. Glaze, Howard P. Goodkin, Sidney M. Gospe, Andrea Grassi, William P. Gray, Renzo Guerrini, Marie-Christine Guiot, William Harkness, Andrew G. Herzog, Linda Huh, Margaret J. Jackson, Thomas S. Jacques, Anna C. Jansen, Sigmund Jenssen, Michael R. Johnson, Dorothy Jones-Davis, Reetta Kälviäinen, Peter W. Kaplan, John F. Kerrigan, Autumn Marie Klein, Matthias Koepp, Edwin H. Kolodny, Kandan Kulandaivel, Ruben I. Kuzniecky, Ahmed Lary, Yolanda Lau, Anna-Elina Lehesjoki, Maria K. Lehtinen, Holger Lerche, Michael P. T. Lunn, Snezana Maljevic, Mark R. Manford, Carla Marini, Bindu Menon, Giulia Milioli, Eli M. Mizrahi, Manish Modi, Márcia Elisabete Morita, Manuel Murie-Fernandez, Vivek Nambiar, Lina Nashef, Vincent Navarro, Aidan Neligan, Ruth E. Nemire, Charles R. J. C. Newton, John O'Donavan, Hirokazu Oguni, Teiichi Onuma, Andre Palmini, Eleni Panagiotakaki, Pasquale Parisi, Elena Parrini, Liborio Parrino, Ignacio Pascual-Castroviejo, M. Scott Perry, Perrine Plouin, Charles E. Polkey, Suresh S. Pujar, Karthik Rajasekaran, R. Eugene Ramsey, Rahul Rathakrishnan, Roberta H. Raven, Guy M. Rémillard, David Rosenblatt, M. Elizabeth Ross, Abdulrahman Sabbagh, P. Satishchandra, Swati Sathe, Ingrid E. Scheffer, Philip A. Schwartzkroin, Rod C. Scott, Frédéric Sedel, Michelle J. Shapiro, Elliott H. Sherr, Michael Shevell, Simon D. Shorvon, Adrian M. Siegel, Gagandeep Singh, S. Sinha, Barbara Spacca, Waney Squier, Carl E. Stafstrom, Bernhard J. Steinhoff, Andrea Taddio, Gianpiero Tamburrini, C. T. Tan, Raymond Y. L. Tan, Erik Taubøll, Robert W. Teasell, Mario Giovanni Terzano, Federica Teutonico, Suzanne A. Tharin, Elizabeth A. Thiele, Pierre Thomas, Paolo Tinuper, Dorothée Kasteleijn-Nolst Trenité, Sumeet Vadera, Pierangelo Veggiotti, Jean-Pierre Vignal, J. M. Walshe, Elizabeth J. Waterhouse, David Watkins, Ruth E. Williams, Yue-Hua Zhang, Benjamin Zifkin, Sameer M. Zuberi
- Edited by Simon D. Shorvon, Frederick Andermann, Renzo Guerrini
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- Book:
- The Causes of Epilepsy
- Published online:
- 05 March 2012
- Print publication:
- 14 April 2011, pp ix-xvi
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Contributors
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- By Susan E. Abbey, James J. Amos, Philip A. Bialer, James A. Bourgeois, Joanne A. Byars, Jaspreet Chahal, Kathy Coffman, Mary Ann Cohen, Catherine Crone, Carlos Fernandez-Robles, Jess G. Fiedorowicz, Mary J. Fitz-Gerald, Gregory Fricchione, Donna Greenberg, Thomas W. Heinrich, Debra R. Kahn, Raheel A. Khan, Robin C. Kopelman, Jeanne M. Lackamp, Joseph A. Locala, Michael Marcangelo, Laura Marsh, Anthony C. Miller, Romina Mizrahi, Megan Moore Brennan, Maryland Pao, John Querques, Davin Quinn, Vani Rao, Robert G. Robinson, Oludamilola Salami, Sanjeev Sockalingam, Sergio E. Starkstein, Scott Stuart, Adrienne Tan, Janeta Tansey, Scott Temple, Alex Thompson, Susan Turkel, Michelle Weckmann, Marcus Wellen, Thomas Wise
- Edited by James J. Amos, University of Iowa, Robert G. Robinson, University of Iowa
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- Book:
- Psychosomatic Medicine
- Published online:
- 04 August 2010
- Print publication:
- 27 May 2010, pp xi-xiv
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