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Page 1811 of Mathematical Reviews Vol. , Issue 96c [page]

1996 Mathematical Reviews  
In the worst case, the size of the repre- sentation is the same as the size of the transitive closure.  ...  For a directed acyclic graph G = (X, U) representing an order P = (X,<p), the preprocessing time complexity is not better than the transitive closure computation cost.  ... 

The Complexity of Andersen's Analysis in Practice [chapter]

Manu Sridharan, Stephen J. Fink
2009 Lecture Notes in Computer Science  
variable and a sparse flow graph.  ...  While the tightest proven worst-case complexity for Andersen's points-to analysis is nearly cubic, the analysis seems to scale better on real-world codes.  ...  Acknowledgments We thank the anonymous reviewers for their helpful comments and Ras Bodík for input on earlier versions of this work.  ... 
doi:10.1007/978-3-642-03237-0_15 fatcat:drvgvornknhlvabzp5eqldoenu

Efficient transitive closure of sparse matrices over closed semirings

Gerald Penn
2006 Theoretical Computer Science  
This paper surveys several alternative data structures and algorithms for multiplying sparse upper-triangular matrices over closed semirings, and evaluates their efficiency in computing transitive closures  ...  of matrices over the Boolean semiring.  ...  Not only does this reduction yield a transitive closure algorithm with the same worst-case complexity as the multiplication algorithm it uses (in the upper-right quadrant), but, with the judicious choice  ... 
doi:10.1016/j.tcs.2005.11.008 fatcat:akifsqu2ljagfkhfk7kcz64pbi

Page 1003 of Mathematical Reviews Vol. 56, Issue 3 [page]

1978 Mathematical Reviews  
For a number of set covering problems, simple algorithms yield worst case ratios which can grow with the log of the problem size.  ...  O(2"), where N is the number of nodes in the graph. The author then provides a simple modification to algorithm A* which never performs worse than A* and in the worst case makes O(N?) expansions.  ... 

Page 6318 of Mathematical Reviews Vol. , Issue 93k [page]

1993 Mathematical Reviews  
For this purpose, we study the worst-case complexity of a nice algorithm. This algorithm is due to Goraltikova and Koubek (1979) and was previously studied by Mehlhorn (1984) and Simon (1988).  ...  We give the first efficient parallel algorithm for finding an approximation to a minimum cycle cover.  ... 

Testing Temporal Connectivity in Sparse Dynamic Graphs [article]

Matthieu Barjon, Arnaud Casteigts, Serge Chaumette, Colette Johnen, Yessin M. Neggaz
2014 arXiv   pre-print
In the case of strict journeys, a number of existing algorithms designed for more general problems can be adapted.  ...  In the case of non-strict journeys, for which no algorithm is known, we show that some pre-processing of the input graph allows us to re-use the same algorithm than before.  ...  Computation of the transitive closure for strict journeys We propose below an algorithm for computing the strict transitive closure G * st in the general case that G is directed.  ... 
arXiv:1404.7634v2 fatcat:nmv7ytdi7rd6dkgfxfyy6gnl3m

Dual Labeling: Answering Graph Reachability Queries in Constant Time

Haixun Wang, Hao He, Jun Yang, P.S. Yu, J.X. Yu
2006 22nd International Conference on Data Engineering (ICDE'06)  
Furthermore, for sparse graphs, the complexity of the labeling process is almost linear, which makes our algorithm applicable to massive datasets.  ...  Analytical and experimental results show that our approach is much more efficient than stateof-the-art approaches.  ...  The Dual-I labeling scheme has constant query time, and for sparse graphs, the labeling complexities of both Dual-I and Dual-II are almost linear.  ... 
doi:10.1109/icde.2006.53 dblp:conf/icde/WangHYYY06 fatcat:5bl6x3vnebaw5ppejlvscpi5iu

Page 6232 of Mathematical Reviews Vol. , Issue 96j [page]

1996 Mathematical Reviews  
Summary: “We propose an approach with a feasible space require- ment to maintain the transitive closure of a class of hypergraphs called OR-graphs.  ...  We also show that a minimal extension to OR-graphs makes the computational complexity of the transitive closure CoNP-complete.”  ... 

Page 6985 of Mathematical Reviews Vol. , Issue 96k [page]

1996 Mathematical Reviews  
The focus of this work is on algorithms and data struc- tures for computing and storing transitive closures of large sparse digraphs which, on the average, would require time and storage space only linear  ...  The space re- quired for storing the transitive closure using the interval represen- tation is just linear in n.  ... 

Giga-scale exhaustive points-to analysis for Java in under a minute

Jens Dietrich, Nicholas Hollingum, Bernhard Scholz
2015 Proceedings of the 2015 ACM SIGPLAN International Conference on Object-Oriented Programming, Systems, Languages, and Applications - OOPSLA 2015  
Any approach must solve an underlying dynamic graph reachability problem, for which the best algorithms have near-cubic worst-case runtime complexity, and, hence, previous work does not scale to programs  ...  In this work, we present a novel approach for solving the field-sensitive points-to problem for Java with the means of (1) a transitive-closure data-structure, and (2) a pre-computed set of potentially  ...  Acknowledgments This project was supported by Oracle Labs, Australia, and ARC grant DP130101970. We would like to thank Cristina  ... 
doi:10.1145/2814270.2814307 dblp:conf/oopsla/DietrichHS15 fatcat:6ntxpumdovevddwvqx6vjy552m

Computing SSA Form with Matrices

Quan Hoang Nguyen, Bernhard Scholz
2007 Electronical Notes in Theoretical Computer Science  
Although there exist efficient graph algorithms for these relations, the algorithms are elaborate to implement.  ...  We implemented our approach in an optimising backend for LCC bytecode and compared its performance with the state-of-the-art approaches.  ...  Acknowledgement We would like to thank Bernd Burgstaller for his useful comments and for proofreading the manuscript.  ... 
doi:10.1016/j.entcs.2007.02.064 fatcat:bxk22ykviveonbtmyeope5blcq

Page 661 of Mathematical Reviews Vol. 55, Issue 2 [page]

1978 Mathematical Reviews  
This paper analyzes a basic recursive algorithm for finding a clique of maximum size in an undirected graph.  ...  , and the construction of linear precedence functions for a grammar of size n in time O(n). Armin Cremers (Bochum) Hyafil, L.; Kung, H. T. The complexity of parallel evaluation of linear recurrence.  ... 

Page 2431 of Mathematical Reviews Vol. , Issue 2004c [page]

2004 Mathematical Reviews  
Summary: “This paper presents an efficient fully dynamic graph al- gorithm for maintaining the transitive closure of a directed graph.  ...  In acyclic graphs, worst case update time is O(n’). In general graphs, the For the web version of Mathematical Reviews, see http: //www.ams.org/mathscinet  ... 

Inferray

Julien Subercaze, Christophe Gravier, Jules Chevalier, Frederique Laforest
2016 Proceedings of the VLDB Endowment  
using ad-hoc optimizations on MSD radix and a custom counting sort; 3) a dedicated temporary storage to perform efficient graph closure computation.  ...  Our measurements on synthetic and real-world datasets show improvements over competitors on RDFS-Plus, and up to several orders of magnitude for transitivity closure.  ...  The authors would also like to thank Satish Nadathur for his help on sorting algorithms, Jacopo Urbani for his help with WebPIE and QueryPIE and the authors of RDFox for their help in configuring their  ... 
doi:10.14778/2904121.2904123 fatcat:6ncfo5nx2zbydihf4dbxlzgc6q

Page 2150 of Mathematical Reviews Vol. , Issue 86e [page]

1986 Mathematical Reviews  
By reduction arguments, similar lower bounds are proved for the majority function and the transitive closure function.  ...  The second finds all the quadrangles in O(a(G)m) time. Since a(G) is at most three for a planar graph G, both run in linear time for a planar graph.  ... 
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