Succinct representations of graphs
Information and Control
Graph-Based Algorithms for Boolean Function Manipulation
IEEE Transactions on Computers
A note on succinct representations of graphs
Information and Control
Implicit representation of graphs
SIAM Journal on Discrete Mathematics
Symbolic model checking: 1020 states and beyond
Information and Computation - Special issue: Selections from 1990 IEEE symposium on logic in computer science
A randomized linear-time algorithm to find minimum spanning trees
Journal of the ACM (JACM)
On the size of binary decision diagrams representing Boolean functions
Theoretical Computer Science
On the effect of local changes in the variable ordering of ordered decision diagrams
Information Processing Letters
A minimum spanning tree algorithm with inverse-Ackermann type complexity
Journal of the ACM (JACM)
Representing graphs implicitly using almost optimal space
Discrete Applied Mathematics - Special issue on international workshop of graph-theoretic concepts in computer science WG'98 conference selected papers
Minimum-weight spanning tree algorithms a survey and empirical study
Computers and Operations Research
An optimal minimum spanning tree algorithm
Journal of the ACM (JACM)
Bisimulation Minimization and Symbolic Model Checking
Formal Methods in System Design
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
The Complexity of Graph Problems fore Succinctly Represented Graphs
WG '89 Proceedings of the 15th International Workshop on Graph-Theoretic Concepts in Computer Science
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
An Algorithm for Strongly Connected Component Analysis in n log n Symbolic Steps
Formal Methods in System Design
On the History of the Minimum Spanning Tree Problem
IEEE Annals of the History of Computing
Representation of graphs by OBDDs
Discrete Applied Mathematics
On the OBDD complexity of the most significant bit of integer multiplication
TAMC'08 Proceedings of the 5th international conference on Theory and applications of models of computation
Exponential space complexity for OBDD-based reachability analysis
Information Processing Letters
Exponential space complexity for symbolic maximum flow algorithms in 0-1 networks
MFCS'10 Proceedings of the 35th international conference on Mathematical foundations of computer science
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
A symbolic approach to the all-pairs shortest-paths problem
WG'04 Proceedings of the 30th international conference on Graph-Theoretic Concepts in Computer Science
Exponential lower bounds on the space complexity of OBDD-Based graph algorithms
LATIN'06 Proceedings of the 7th Latin American conference on Theoretical Informatics
Implicit enumeration of strongly connected components and an application to formal verification
IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems
Priority functions for the approximation of the metric TSP
Information Processing Letters
| Hi-index | 5.23 |
The minimum spanning tree problem is one of the most fundamental algorithmic graph problems and OBDDs are a very common dynamic data structure for Boolean functions. 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 OBDD-represented graph instances. Here, a symbolic minimum spanning tree algorithm using O(log^3|V|) functional operations is presented, where V is the set of vertices of the input graph. Moreover, the computation of the transitive closure is investigated and it is proved that there can be an exponential blow-up from input to output size. Furthermore, answering an open problem posed by Sawitzki [37] it is shown that every symbolic OBDD-based algorithm for the minimum spanning tree problem needs exponential space (with respect to the OBDD size of the input graph). This result even holds for planar input graphs.