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Symbolic topological sorting with OBDDs

2006
*
Journal of Discrete Algorithms
*

We present a

doi:10.1016/j.jda.2005.01.008
fatcat:rgfxj22ewnbxzdcrtchlrlj22e
*symbolic**OBDD*algorithm for*topological**sorting*which requires O(log 2 |V |)*OBDD*operations. ... This is the first true runtime analysis of a*symbolic**OBDD*algorithm for a fundamental graph problem, and it demonstrates that one can hope that the algorithm behaves well for sufficiently structured inputs ... We use the*symbol*for the corresponding relation, i.e., v w if v precedes w. In the following we describe a*symbolic**OBDD*-algorithm which*topologically**sorts*the vertices according to the relation . ...##
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Symbolic Topological Sorting with OBDDs
[chapter]

2003
*
Lecture Notes in Computer Science
*

We present a

doi:10.1007/978-3-540-45138-9_61
fatcat:zqt7qyfztvbrdewmhqr76y3mzy
*symbolic**OBDD*algorithm for*topological**sorting*which requires O(log 2 |V |)*OBDD*operations. ... This is the first true runtime analysis of a*symbolic**OBDD*algorithm for a fundamental graph problem, and it demonstrates that one can hope that the algorithm behaves well for sufficiently structured inputs ... We use the*symbol*for the corresponding relation, i.e., v w if v precedes w. In the following we describe a*symbolic**OBDD*-algorithm which*topologically**sorts*the vertices according to the relation . ...##
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On symbolic OBDD-based algorithms for the minimum spanning tree problem

2012
*
Theoretical Computer Science
*

Furthermore, answering an open problem posed by Sawitzki [37] it is shown that every

doi:10.1016/j.tcs.2011.11.029
fatcat:a5efmdgy6rabzcfamunpsddnbq
*symbolic**OBDD*-based algorithm for the minimum spanning tree problem needs exponential space (*with*respect to the*OBDD*... Since in some applications graphs become larger and larger, a research branch has emerged which is concerned*with*the design and analysis of so-called*symbolic*algorithms for classical graph problems on ... In [36, 43]*symbolic*algorithms for maximum flow in 0-1 networks and*topological**sorting*have been presented and afterward analyzed for a restricted graph class. ...##
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What Graphs can be Efficiently Represented by BDDs?

2007
*
2007 International Conference on Computing: Theory and Applications (ICCTA'07)
*

For randomly generated dense graphs, the gain, i. e., the ratio of the number of graph edges to the

doi:10.1109/iccta.2007.133
dblp:conf/iccta/DongM07
fatcat:v4lozcczkzbtno4xeprtviwgda
*OBDD*size, increases*with*the number of vertices and the density of the graphs. ... We have carried out experimental research into implicit representation of large graphs using reduced ordered binary decision diagrams (*OBDDs*). ... That is the reason that researchers began to think about*OBDD*based*symbolic*graph algorithms, e. g.,*symbolic**topological**sorting*[17] ,*symbolic*computation of strongly connected components [6] and ...##
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Subject Index

2006
*
Journal of Discrete Algorithms
*

*sorting*

*Symbolic*

*topological*

*sorting*

*with*

*OBDDs*, 51 Traveling Salesman problem An improved approximation algorithm for the asymmetric TSP

*with*strengthened triangle inequality, 623 Turing reduction Polynomial ... few vertices of large degree, 201 Implicit graph algorithms

*Symbolic*

*topological*

*sorting*

*with*

*OBDDs*, 51 Information visualization A framework and algorithms for circular drawings of graphs, 25 ...

##
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Symbolic Graphs: Linear Solutions to Connectivity Related Problems

2007
*
Algorithmica
*

The importance of

doi:10.1007/s00453-007-9079-5
fatcat:gbrx2nuv2fbrlb2s5j2koax3vu
*symbolic*data structures such as Ordered Binary Decision Diagrams (*OBDD*) is rapidly growing in many areas of Computer Science where the large dimensions of the input models is a challenging ... However,*OBDD*representations pose strict constraints in the algorithm design issue. ... Finally, the authors in [33, 34, 44] , developed a number of*symbolic*graph algorithms (*topological**sorting*[44] , max-flow on 0-1 networks, all pair shortest paths problem [34] ) all relying on*symbolic*...##
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A Symbolic Approach to the All-Pairs Shortest-Paths Problem
[chapter]

2004
*
Lecture Notes in Computer Science
*

Graphs can be represented

doi:10.1007/978-3-540-30559-0_13
fatcat:77ef2obn5vhdxaq2a3rxhzv424
*symbolically*by the Ordered Binary Decision Diagram (*OBDD*) of their characteristic function. ... It requires Θ log 2 (NB)*OBDD*-operations to obtain the lengths and edges of all shortest paths in graphs*with*N nodes and maximum edge weight B. ... used in the analysis of*symbolic**topological**sorting*[26] and maximum flow algorithms [20] [21] [22] . ...##
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On Symbolic Representations of Maximum Matchings and (Un)directed Graphs
[chapter]

2010
*
IFIP Advances in Information and Communication Technology
*

Here, it is shown that

doi:10.1007/978-3-642-15240-5_21
fatcat:jt3eheplcvgc7peqfd3d54bg2q
*symbolic**OBDD*-based algorithms for the maximum matching problem need exponential space (*with*respect to the*OBDD*size of the input graph). ... Since in some applications graphs become larger and larger, a research branch has emerged which is concerned*with*the theoretical design and analysis of so-called*symbolic*algorithms for classical graph ... In [21] and [28]*symbolic*algorithms for maximum flow in 0-1 networks and*topological**sorting*have been presented which have polylogarithmic running time*with*respect to the number of vertices of a ...##
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Design and Evaluation of a Symbolic and Abstraction-Based Model Checker
[chapter]

2004
*
Lecture Notes in Computer Science
*

In case of properties expressed

doi:10.1007/978-3-540-30476-0_19
fatcat:bdg6dji5ebdk5od5sysvfmpu4e
*with*a linear time logic, it appears that the second step is often more time consuming than the first one. ... In this work, we present a mixed solution which builds an observation graph represented in a non*symbolic*way but where the nodes are essentially*symbolic*set of states. ... Then we check the existence of dead states*with*the help of the*symbolic*operation Enab (via DetectDead) and the existence of a loop of unobserved events by applying a kind of*topologic**sort*of the underlying ...##
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Lower Bounds on the OBDD Size of Graphs of Some Popular Functions
[chapter]

2005
*
Lecture Notes in Computer Science
*

Therefore, we consider fundamental arithmetic and storage access functions

doi:10.1007/978-3-540-30577-4_33
fatcat:yegdsrhrubcqdasqxzuxiisgfy
*with*exponential*OBDD*size and transfer these results to the graphs of these functions. ... In order to investigate the limits of*symbolic*graph algorithms which work on*OBDD*-represented graph instances, it is useful to have simply-structured graphs whose*OBDD*representation has exponential size ... Until now,*symbolic*methods for flow maximization [11, 22] ,*topological**sorting*[30] , shortest paths computation [21, 24] , and component analysis [7, 8] have been presented. ...##
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OBDD-Based Representation of Interval Graphs
[article]

2013
*
arXiv
*
pre-print

Given the

arXiv:1305.2772v1
fatcat:tezy3h3dkjgg5ld5rmvtzxxebi
*OBDD*as an input,*symbolic*/implicit*OBDD*-based graph algorithms can solve optimization problems by mainly using functional operations, e.g. quantification or binary synthesis. ... In this paper, we show that the*OBDD*size of unit interval graphs is O( | V | / | V |) and the*OBDD*size of interval graphs is O(| V | | V |) which both improve a known result from Nunkesser and Woelfel ... Acknowledgements I thank Beate Bollig, Melanie Schmidt and Chris Schwiegelshohn for the valuable discussions and, together*with*the anonymous referees, for their comments on the presentation of the paper ...##
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OBDD-Based Representation of Interval Graphs
[chapter]

2013
*
Lecture Notes in Computer Science
*

Given the

doi:10.1007/978-3-642-45043-3_25
fatcat:mf3pqnybxvhcrk6ffd6kcpr2ia
*OBDD*as an input,*symbolic*/implicit*OBDD*-based graph algorithms can solve optimization problems by mainly using functional operations, e. g., quantification or binary synthesis. ... In this paper, we show that the*OBDD*size of unit interval graphs is O(|V |/ log |V |) and the*OBDD*size of interval graphs is O(|V | log |V |) which both improve a known result from Nunkesser and Woelfel ... Acknowledgements I thank Beate Bollig, Melanie Schmidt and Chris Schwiegelshohn for the valuable discussions and, together*with*the anonymous referees, for their comments on the presentation of the paper ...##
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Treewidth in Verification: Local vs. Global
[chapter]

2005
*
Lecture Notes in Computer Science
*

Cutwidth boundedness is used also to improve

doi:10.1007/11591191_34
fatcat:wxahogt3vngi7parbqynjm6yuq
*symbolic*simulation and Boolean satisfiability in [4, 29] . ... For example, it is easy to see that the graphs underlying systems*with*two counters are essentially grids, which are known to have high treewidth [26] . ...*OBDDs*are often used to perform*symbolic*image operations, which requires applying existential quantification to*OBDDs*[20] . ...##
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An efficient algorithm for computing bisimulation equivalence

2004
*
Theoretical Computer Science
*

The proposed algorithm is then re-elaborated to produce a

doi:10.1016/s0304-3975(03)00361-x
fatcat:cuqldmdca5bezfrxu5eqfejjvy
*symbolic*version. ... We propose an e cient algorithmic solution to the problem of determining a Bisimulation Relation on a ÿnite structure working both on the explicit and on the implicit (*symbolic*) representation. ... Acknowledgements We thank Nadia Ugel for her C implementation and many useful discussions, and Ra aella Gentilini and Elio Panegai for their contribution in the development and implementation of the*Symbolic*...##
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Combinational logic synthesis for LUT based field programmable gate arrays

1996
*
ACM Transactions on Design Automation of Electronic Systems
*

and 4-LUTs, which can also be combined to form 5-LUTs; the AT&T ORCA2C [AT&T 1995] supplies 4-LUTs that can be combined to form 5-LUTs and 6-LUTs), most studies assume a homogeneous LUT architecture

doi:10.1145/233539.233540
fatcat:q62vuvv565h6hmzkfp67be6urm
*with*...*OBDD*Based Extraction. If the node function f is represented by*OBDD*, let v be a nonterminal*with*associated subfunction f v . The sub-*OBDD*rooted at v defines f v . ... Similarly, if the function is represented by an*OBDD*, decomposition can be performed by subgraph splitting. We regard such operations as*symbolic*decompositions in general. ...
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