Graph-Based Algorithms for Boolean Function Manipulation
IEEE Transactions on Computers
Re-encoding sequential circuits to reduce power dissipation
ICCAD '94 Proceedings of the 1994 IEEE/ACM international conference on Computer-aided design
Algebraic decision diagrams and their applications
ICCAD '93 Proceedings of the 1993 IEEE/ACM international conference on Computer-aided design
Symbolic manipulation of Boolean functions using a graphical representation
DAC '85 Proceedings of the 22nd ACM/IEEE Design Automation Conference
To split or to conjoin: the question in image computation
Proceedings of the 37th Annual Design Automation Conference
Implicit enumeration of strongly connected components
ICCAD '99 Proceedings of the 1999 IEEE/ACM international conference on Computer-aided design
All-Pairs Almost Shortest Paths
SIAM Journal on Computing
Journal of Algorithms
Logic Synthesis and Verification Algorithms
Logic Synthesis and Verification Algorithms
A Symbolic Algorithms for Maximum Flow in 0-1 Networks
Formal Methods in System Design
Computing strongly connected components in a linear number of symbolic steps
SODA '03 Proceedings of the fourteenth annual ACM-SIAM symposium on Discrete algorithms
A Comparative Study of Symbolic Algorithms for the Computation of Fair Cycles
FMCAD '00 Proceedings of the Third International Conference on Formal Methods in Computer-Aided Design
An Algorithm for Strongly Connected Component Analysis in n log n Symbolic Steps
FMCAD '00 Proceedings of the Third International Conference on Formal Methods in Computer-Aided Design
Complexity of Problems on Graphs Represented as OBDDs (Extended Abstract)
STACS '98 Proceedings of the 15th Annual Symposium on Theoretical Aspects of Computer Science
BDD-Based Cryptanalysis of Keystream Generators
EUROCRYPT '02 Proceedings of the International Conference on the Theory and Applications of Cryptographic Techniques: Advances in Cryptology
Efficient omega-Regular Language Containment
CAV '92 Proceedings of the Fourth International Workshop on Computer Aided Verification
Fine-Grain Conjunction Scheduling for Symbolic Reachability Analysis
TACAS '02 Proceedings of the 8th International Conference on Tools and Algorithms for the Construction and Analysis of Systems
Lower bounds on the OBDD size of two fundamental functions' graphs
Information Processing Letters
State-set branching: Leveraging BDDs for heuristic search
Artificial Intelligence
Representation of graphs by OBDDs
Discrete Applied Mathematics
The complexity of problems on implicitly represented inputs
SOFSEM'06 Proceedings of the 32nd conference on Current Trends in Theory and Practice of Computer Science
Representation of graphs by OBDDs
ISAAC'05 Proceedings of the 16th international conference on Algorithms and Computation
Lower bounds on the OBDD size of graphs of some popular functions
SOFSEM'05 Proceedings of the 31st international conference on Theory and Practice of Computer Science
On symbolic scheduling independent tasks with restricted execution times
WEA'05 Proceedings of the 4th international conference on Experimental and Efficient Algorithms
On the OBDD size for graphs of bounded tree- and clique-width
IWPEC'06 Proceedings of the Second international conference on Parameterized and Exact Computation
Exponential lower bounds on the space complexity of OBDD-Based graph algorithms
LATIN'06 Proceedings of the 7th Latin American conference on Theoretical Informatics
On symbolic OBDD-based algorithms for the minimum spanning tree problem
Theoretical Computer Science
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Graphs can be represented symbolically by the Ordered Binary Decision Diagram (OBDD) of their characteristic function. To solve problems in such implicitly given graphs, specialized symbolic algorithms are needed which are restricted to the use of functional operations offered by the OBDD data structure. In this paper, a symbolic algorithm for the all-pairs shortest-paths (APSP) problem in loopless directed graphs with strictly positive integral edge weights is presented. It requires $\Theta\bigl(\log^{2}(NB)\bigr)$ OBDD-operations to obtain the lengths and edges of all shortest paths in graphs with N nodes and maximum edge weight B. It is proved that runtime and space usage are polylogarithmic w. r. t. N and B on graph sequences with characteristic bounded-width functions. This convenient property is closed under certain graph composition operations. Moreover, an alternative symbolic approach for general integral edge weights is sketched which does not behave efficiently on general graph sequences with bounded-width functions. Finally, two variants of the APSP problem are briefly discussed.