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Abstract: It is shown that the problem of maintaining the topological order of the nodes of a directed acyclic graph while inserting m edges can be solved in O(min{m log n}) time, an improvement over the best known result of O(mn). In addition, we analyze the complexity of the same algorithm with respect to the treewidth k of the underlying undirected graph. We show that the algorithm runs in time O(mk log n) for general k and that it can be implemented to run in O(n log n) time on trees,... (Update)
Context of citations to this paper: More
.... Phase II of the algorithm: Very recently, the notion of f cost was introduced as a more refined measure for the quality of a tree decomposition [12]. Here, f : N R is some function and the f cost of a tree decomposition is defined to be # i#I f( X i ) Since, in Phase II,...
Cited by: More
Tree Decompositions of Graphs: Saving Memory in Dynamic .. - Betzler, Niedermeier.. (2004) (Correct)
Experimental Evaluation of a Tree Decomposition Based.. - Alber, Dorn, Niedermeier (2002) (Correct)
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1.5: Online Topological Ordering - Katriel, Bodlaender (Correct)
0.5: A Dynamic Algorithm for Topologically Sorting Directed Acyclic .. - Pearce, Kelly (2004) (Correct)
0.2: Online Algorithms for Topological Order and Strongly Connected.. - Pearce (2003) (Correct)
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BibTeX entry: (Update)
H. L. Bodlaender and F. V. Fomin. Tree decompositions with small cost. In Proceedings 8th SWAT 2002. http://citeseer.ist.psu.edu/article/bodlaender05tree.html More
@misc{ bodlaender02tree,
author = "H. Bodlaender and F. Fomin",
title = "Tree decompositions with small cost",
text = "H. L. Bodlaender and F. V. Fomin. Tree decompositions with small cost.
In Proceedings 8th SWAT 2002.",
year = "2002",
url = "citeseer.ist.psu.edu/article/bodlaender05tree.html" }
Citations (may not include all citations):405 Depth first search and linear graph algorithms (context) - Tarjan - 1972
353 Fibonacci heaps and their uses in improved network optimizat.. (context) - Fredman, Tarjan - 1987
143 Algorithmic aspects of tree-width (context) - Robertson, Seymour - 1986
127 arboretum of graphs with bounded treewidth (context) - Bodlaender, k- - 1998
99 Two algorithms for maintaining order in a list (context) - Dietz, Sleator - 1987
49 Incremental evaluation of computational circuits (context) - Alpern, Hoover et al. - 1990
26 the computational complexity of dynamic graph problems - Ramalingam, Reps - 1996
16 Two simplified algorithms for maintaining order in a list - Bender, Cole et al. - 2002
11 A Constraint-Based Architecture for Local Search - Michel, Van Hentenryck - 2002
9 On competitive on-line algorithms for the dynamic priority-o.. (context) - Ramalingam, Reps - 1994
8 Maintaining a topological order under edge insertions (context) - Marchetti-Spaccamela, Nanni et al. - 1996
4 On algorithms for online topological ordering and sorting (context) - Katriel - 2004
4 Sather language compilerdebugger implementation (context) - Lim, Sather et al. - 1992
3 A dynamic algorithm for topologically sorting directed acycl.. - Pearce, Kelly - 2004
3 line graph algorithms for incremental compilation (context) - Marchetti-Spaccamela, Nanni et al. - 1993
Documents on the same site (http://www.cs.uu.nl/research/techreps/grp/jvl.html): More
Comparing Loop Cutsets and Clique Trees in Probabilistic.. - van der Gaag, Bodlaender (1997) (Correct)
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Linear Election for Oriented Hypercubes - Gerard Tel Department (1993) (Correct)
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