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On the random walk method for protocol testing [chapter]

Milena Mihail, Christos H. Papadimitriou
1994 Lecture Notes in Computer Science  
Following West's original reasoning, efficient sampling of the reachable state space by random walk suffices to ensure effectiveness of testing.  ...  In the context of Markov chain theory, "small cover time" can be thought of as a simpler justification for the effectiveness of testing by random walk; all symmetric (reversible) protocols possess the  ...  Although the expressibility of SSDF's is rather restricted, in the sense that their reachable state spaces have fairly regular characterizations, the transition graph over the reachable state space is  ... 
doi:10.1007/3-540-58179-0_49 fatcat:eln5zuyuibewld4gorwanpmjsi

Improved Dynamic Reachability Algorithms for Directed Graphs

Liam Roditty, Uri Zwick
2008 SIAM journal on computing (Print)  
We obtain several new dynamic algorithms for maintaining the transitive closure of a directed graph, and several other algorithms for answering reachability queries without explicitly maintaining a transitive  ...  Among our algorithms are: (i) A decremental algorithm for maintaining the transitive closure of a directed graph, through an arbitrary sequence of edge deletions, in Ç´ÑÒµ total expected time, essentially  ...  Concluding remarks and open problems We presented an essentially optimal decremental algorithm for maintaining the transitive closure of a general graph.  ... 
doi:10.1137/060650271 fatcat:xwkqu4z4onhxpiz5nv6p4sf5wi

The Assembly of Ecological Communities: A Minimalist Approach

Luh Hang-Kwang, Stuart L. Pimm
1993 Journal of Animal Ecology  
Persistent cycles are rare in the random graphs and are impossible in the landscape graphs. 6. Persistent states are nearly always reachable from the empty community in the random graphs.  ...  In the random transition graphs, the directions of the transitions are specified entirely at random. In the second recipe, we exclude all cycles by assigning each state a random ‘height.’  ... 
doi:10.2307/5394 fatcat:sq2ge4iflzb43gia6mhzxotw6i

Trade-offs for fully dynamic transitive closure on DAGs: breaking through the O(n2 barrier

Camil Demetrescu, Giuseppe F. Italiano
2005 Journal of the ACM  
We present an algorithm for directed acyclic graphs that breaks through the O(n 2 ) barrier on the single-operation complexity of fully dynamic transitive closure, where n is the number of edges in the  ...  graph.  ...  of fully dynamic transitive closure in the case of directed acyclic graphs.  ... 
doi:10.1145/1059513.1059514 fatcat:xpsgkq5ldbhxbexsp2om23cxe4

Balanced FSM Generation for Empirical Studies

Sarah Salahuddin, Kirill Bogdanov, Neil Walkinshaw
2008 2008 IEEE International Conference on Software Testing Verification and Validation Workshop  
It is also possible to build machines where a user-defined proportion of states have a few times higher number of incoming/outgoing transitions.  ...  The novelty of the work is generation of what we call "balanced", state machines where the number of incoming and outgoing transitions from each state is a parameter specified by a user.  ...  Unlike the random graph generation algorithms discussed earlier these are "balanced" graphs and not entirely random in their nature.  ... 
doi:10.1109/icstw.2008.9 dblp:conf/icst/SalahuddinBW08 fatcat:ppyjpdtgizf2tglshzrk7mu5wm

Internet resiliency to attacks and failures under BGP policy routing

Danny Dolev, Sugih Jamin, Osnat (Ossi) Mokryn, Yuval Shavitt
2006 Computer Networks  
The agreements impose policies that govern routing in the AS level, and thus the resulting topology graph is directed, and thus the reachability between Ases is not transitive.  ...  We show, using partial views obtained from the Internet, that the Internet's resiliency to a deliberate attack is much smaller than previously found, and its reachability is also somewhat lower under random  ...  Acknowledgements This research was supported in part by a grant from the United States-Israel Binational Science Foundation (BSF), Jerusalem, Israel; by a grant from the Israel Science Foundation (ISF)  ... 
doi:10.1016/j.comnet.2005.11.010 fatcat:6gtecf37izfijascg2rm352lly

On the random structure of behavioural transition systems

Jan Friso Groote, Remco van der Hofstad, Matthias Raffelsieper
2016 Science of Computer Programming  
This research was in part supported by NWO and Agentschap NL. Related Work. As far as we know, there is not much work on the random structure of transition systems representing behaviour.  ...  Estimating the size of a Petri Net's state space has been investigated in [11] .  ...  Note that the number of reachable states is at most N. This paper considers state spaces being the graph product of two or more random transition systems.  ... 
doi:10.1016/j.scico.2016.02.006 fatcat:qdj3hsw4u5etjh4nwnzinsgsj4

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)  
Our scheme ensures that graph reachability queries can be answered in constant time.  ...  However, the labeling process itself is often too time consuming to be practical for large graphs. In this paper, we propose a novel labeling scheme for sparse graphs.  ...  It answers reachability query in constant time but need O(n 2 ) space to store the transitive closure of an nvertex graph.  ... 
doi:10.1109/icde.2006.53 dblp:conf/icde/WangHYYY06 fatcat:5bl6x3vnebaw5ppejlvscpi5iu

Hit-or-Jump: An Algorithm for Embedded Testing with Applications to in Services [chapter]

Ana Cavalli, David Lee, Christian Rinderknecht, Fatiha Zaïdi
1999 IFIP Advances in Information and Communication Technology  
It does not have state space explosion, as is often encountered in exhaustive search, and it quickly covers the system components under test without being "trapped", as is experienced by random walks.  ...  The algorithm has been implemented and applied to embedded testing of telephone services in an Intelligent Network (IN) architecture, including the Basic Call Service and five supplementary services.  ...  Among all the possible outgoing edges in the reachability graph from the initial node, we select one uniformly at random, and follow that edge to the next node in the reachability graph.  ... 
doi:10.1007/978-0-387-35578-8_3 fatcat:jdmldks2mje4pn267afcfndaku

Average case analysis of fully dynamic reachability for directed graphs

Paola Alimonti, Stefano Leonardi, Alberto Marchetti-Spaccamela
1996 RAIRO - Theoretical Informatics and Applications  
Our algorithms perform favorably with the best known algrithms for Computing the transitive closure in random graphs [14, 15] .  ...  The data structure for reach queries given in Section 3.2 does not easily extend to semi-random directed graphs since the algorithm given in [14] for Computing the transitive closure in random directed  ... 
doi:10.1051/ita/1996300403051 fatcat:spi2b7odifd7neaqhfvf3m47si

Random walks in time-graphs

Utku Günay Acer, Petros Drineas, Alhussein A. Abouzeid
2010 Proceedings of the Second International Workshop on Mobile Opportunistic Networking - MobiOpp '10  
random walk on this graph has a small hitting time.  ...  The notion of connectivity in time-graphs is fundamentally different than that in static graphs.  ...  Any opinions, findings, and conclusions or recommendations expressed in this material are those of the authors and do not necessarily reflect the views of the National Science Foundation.  ... 
doi:10.1145/1755743.1755761 dblp:conf/mobiopp/AcerDA10 fatcat:6atgcynnbzfuvj466rlv6tsp3e

GRAIL

Hilmi Yildirim, Vineet Chaoji, Mohammed J. Zaki
2010 Proceedings of the VLDB Endowment  
We present a very simple, but scalable reachability index, called GRAIL, that is based on the idea of randomized interval labeling, and that can effectively handle very large graphs.  ...  GRAIL has linear indexing time and space, and the query time ranges from constant time to being linear in the graph order and size.  ...  In this paper we present a novel, scalable graph indexing approach for very large graphs, called GRAIL, which stands for Graph Reachability Indexing via RAndomized Interval Labeling.  ... 
doi:10.14778/1920841.1920879 fatcat:6gsy7bpfbfhzfaddqq6hmiq5ny

Fault-tolerant routing on Borel Cayley graph

Junghun Ryu, Eric Noel, K. Wendy Tang
2012 2012 IEEE International Conference on Communications (ICC)  
In this paper, we explore the use of a pseudo-random graph family, Borel Cayley graph family, as the network topology in an NGN (Next Generation Network) with thousands of nodes operated in a packet switching  ...  Our algorithm exploits the vertex-transitivity property of Borel Cayley graphs and relies on extra information to reflect topology change.  ...  Any opinions, findings and conclusions or recommendations expressed in this article are those of the authors and do not necessarily reflect the views of the National Science Foundation.  ... 
doi:10.1109/icc.2012.6364037 dblp:conf/icc/RyuNT12 fatcat:flyuqeiasrhzxacdirocpj7cdm

Simple, fast, and scalable reachability oracle

Ruoming Jin, Guan Wang
2013 Proceedings of the VLDB Endowment  
On large graphs, their index sizes and their query performance can now beat the state-of-the-art transitive closure compression and online search approaches.  ...  Despite their simplicity and elegance, reachability oracles have failed to achieve efficiency in more than ten years since their introduction: The main problem is high construction cost, which stems from  ...  Here k is set to be the total number of vertices in the graph for the basic reachability. 5) GRAIL (GL) [38] , a scalable reachability indexing approach using random DFS labeling (the number of intervals  ... 
doi:10.14778/2556549.2556578 fatcat:yn6omi2a4bebtoaxl7z3d6kffm

Analyzing Gene Relationships for Down Syndrome with Labeled Transition Graphs

Neha Rungta, Hyrum Carroll, Eric G Mercer, Randall J. Roper, Mark Clement, Quinn Snell
2007 Formal Methods in Computer Aided Design (FMCAD'07)  
This work links chromosome 21 genes to non-chromosome 21 genes known to interact in a Down syndrome phenotype through a reachability analysis of labeled transition graphs extracted from published gene  ...  The analysis provides new relations in a recently discovered link between a specific gene and Down syndrome phenotype.  ...  We perform an exhaustive reachability analysis on the graph using a randomized breadth-first search (BFS).  ... 
doi:10.1109/fmcad.2007.4402003 fatcat:jvdeudauhjeqxdld7b4us52x6e
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