PL EN


Preferencje help
Widoczny [Schowaj] Abstrakt
Liczba wyników
2004 | 24 | 1 | 137-145
Tytuł artykułu

A simple linear algorithm for the connected domination problem in circular-arc graphs

Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
A connected dominating set of a graph G = (V,E) is a subset of vertices CD ⊆ V such that every vertex not in CD is adjacent to at least one vertex in CD, and the subgraph induced by CD is connected. We show that, given an arc family F with endpoints sorted, a minimum-cardinality connected dominating set of the circular-arc graph constructed from F can be computed in O(|F|) time.
Wydawca
Rocznik
Tom
24
Numer
1
Strony
137-145
Opis fizyczny
Daty
wydano
2004
otrzymano
2002-03-18
poprawiono
2003-01-18
Twórcy
autor
  • Department of Computer Science and Information Engineering, National Chung Cheng University, Ming-Hsiung, Chiayi 621, Taiwan, R.O.C.
  • Department of Computer Science and Information Engineering, National Chung Cheng University, Ming-Hsiung, Chiayi 621, Taiwan, R.O.C.
Bibliografia
  • [1] M.J. Atallah, D.Z. Chen, and D.T. Lee, An optimal algorithm for shortest paths on weighted interval and circular-arc graphs, with applications, Algorithmica 14 (1995) 429-441, doi: 10.1007/BF01192049.
  • [2] M.S. Chang, Efficient algorithms for the domination problems on interval and circular-arc graphs, SIAM J. Comput. 27 (1998) 1671-1694, doi: 10.1137/S0097539792238431.
  • [3] M.S. Chang, Weighted domination of cocomparability graphs, Discrete Appl. Math. 80 (1997) 135-147, doi: 10.1016/S0166-218X(97)80001-7.
  • [4] D.Z. Chen, D.T. Lee, R. Sridhar, and C.N. Sekharan, Solving the all-pair shortest path query problem on interval and circular-arc graphs, Networks 31 (1998) 249-258, doi: 10.1002/(SICI)1097-0037(199807)31:4<249::AID-NET5>3.0.CO;2-D
  • [5] E.M. Eschen and J. Spinrad, An O(n²) algorithm for circular-arc graph recognition, in: Proceedings of the 4th Annual ACM-SIAM Symposium on Discrete Algorithm SODA'93 (1993) 128-137.
  • [6] M.R. Garey and D.S. Johnson, Computers and Intractability: A Guide to the Theory of NP-Completeness (W.H. Freeman, San Francisco, CA, 1979).
  • [7] M.C. Golumbic, Algorithmic Graph Theory and Perfect Graphs (Academic Press, New York, 1980).
  • [8] M.C. Golumbic and P.L. Hammer, Stability in circular arc graphs, J. Algorithms 9 (1988) 314-320, doi: 10.1016/0196-6774(88)90023-5.
  • [9] T.W. Haynes, S.T. Hedetniemi, and P.J. Slater, Fundamentals of Domination in Graphs (Marcel Dekker, New York, 1998).
  • [10] T.W. Haynes, S.T. Hedetniemi, and P.J. Slater, Domination in Graphs - Advanced Topics (Marcel Dekker, New York, 1998).
  • [11] W.L. Hsu, O(M·N) algorithms for the recognization and isomorphism problems on circular-arc graphs, SIAM J. Comput. 24 (1995) 411-439, doi: 10.1137/S0097539793260726.
  • [12] W.L. Hsu and K.H. Tsai, Linear time algorithms on circular-arc graphs, Inform. Process. Lett. 40 (1991) 123-129, doi: 10.1016/0020-0190(91)90165-E.
  • [13] J.M. Keil, The complexity of domination problems in circle graphs, Discrete Appl. Math. 42 (1993) 51-63, doi: 10.1016/0166-218X(93)90178-Q.
  • [14] J.M. Keil and D. Schaefer, An optimal algorithm for finding dominating cycles in circular-arc graphs, Discrete Appl. Math. 36 (1992) 25-34, doi: 10.1016/0166-218X(92)90201-K.
  • [15] E. Köhler, Connected domination and dominating clique in trapezoid graphs, Discrete Appl. Math. 99 (2000) 91-110, doi: 10.1016/S0166-218X(99)00127-4.
  • [16] R. Laskar and J. Pfaff, Domination and irredundance in split graphs, Technical Report 430, Dept. Mathematical Sciences (Clemson University, 1983).
  • [17] C.C. Lee and D.T. Lee, On a circle-cover minimization problem, Inform. Process. Lett. 18 (1984) 109-115, doi: 10.1016/0020-0190(84)90033-4.
  • [18] Y.L. Lin, F.R. Hsu, and Y.T. Tsai, Efficient algorithms for the minimum connected domination on trapezoid graphs, Lecture Notes in Comput. Sci. 1858 (Springer Verlag, 2000) 126-136.
  • [19] G.K. Manacher and T.A. Mankus, A simple linear time algorithm for finding a maximum independent set of circular arcs using intervals alone, Networks 39 (2002) 68-72, doi: 10.1002/net.10014.
  • [20] S. Masuda and K. Nakajima, An optimal algorithm for finding a maximum independent set of a circular-arc graph, SIAM J. Comput. 17 (1988) 41-52, doi: 10.1137/0217003.
  • [21] R.M. McConnell, Linear-time recognition of circular-arc graphs, in: Proceedings of the 42nd IEEE Symposium on Foundations of Computer Science FOCS'01 (2001) 386-394.
  • [22] M. Moscarini, Doubly chordal graphs, Steiner trees, and connected domination, Networks 23 (1993) 59-69, doi: 10.1002/net.3230230108.
  • [23] H. Müller and A. Brandstädt, The NP-completeness of Steiner tree and dominating set for chordal bipartite graphs, Theoret. Comput. Sci. 53 (1987) 257-265, doi: 10.1016/0304-3975(87)90067-3.
  • [24] J. Pfaff, R. Laskar, and S.T. Hedetniemi, NP-completeness of total and connected domination, and irredundance for bipartite graphs, Technical Report 428, Dept. Mathematical Sciences (Clemson University, 1983).
  • [25] A. Tucker, An efficient test for circular-arc graphs, SIAM J. Comput. 9 (1980) 1-24, doi: 10.1137/0209001.
  • [26] H.G. Yeh and G.J. Chang, Weighted connected domination and Steiner trees in distance-hereditary graphs, Discrete Appl. Math. 87 (1998) 245-253, doi: 10.1016/S0166-218X(98)00060-2.
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.bwnjournal-article-doi-10_7151_dmgt_1220
JavaScript jest wyłączony w Twojej przeglądarce internetowej. Włącz go, a następnie odśwież stronę, aby móc w pełni z niej korzystać.