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
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
Branching programs and binary decision diagrams: theory and applications
Branching programs and binary decision diagrams: theory and applications
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
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
On the History of the Minimum Spanning Tree Problem
IEEE Annals of the History of Computing
Representation of graphs by OBDDs
Discrete Applied Mathematics
Symbolic OBDD-Based Reachability Analysis Needs Exponential Space
SOFSEM '10 Proceedings of the 36th Conference on Current Trends in Theory and Practice of Computer Science
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 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
Exponential lower bounds on the space complexity of OBDD-Based graph algorithms
LATIN'06 Proceedings of the 7th Latin American conference on Theoretical Informatics
An efficient implicit OBDD-Based algorithm for maximal matchings
LATA'12 Proceedings of the 6th international conference on Language and Automata Theory and Applications
Implicit computation of maximum bipartite matchings by sublinear functional operations
TAMC'12 Proceedings of the 9th Annual international conference on Theory and Applications of Models of Computation
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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(log3 |V|) functional operations is presented, where V is the set of vertices of the input graph. Furthermore, answering an open problem posed by Sawitzki (2006) 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.