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
Limits to parallel computation: P-completeness theory
Limits to parallel computation: P-completeness theory
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
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
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
Parameterized Complexity
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
On symbolic OBDD-based algorithms for the minimum spanning tree problem
COCOA'10 Proceedings of the 4th international conference on Combinatorial optimization and applications - Volume Part II
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
On symbolic OBDD-based algorithms for the minimum spanning tree problem
Theoretical Computer Science
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
Priority functions for the approximation of the metric TSP
Information Processing Letters
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Highly regular data can be represented succinctly by various kinds of implicit data structures. Many problems in P are known to be hard if their input is given as circuit or Ordered Binary Decision Diagram (OBDD). Nevertheless, in practical areas like CAD and Model Checking, symbolic algorithms using functional operations on OBDD-represented data are well-established. Their theoretical analysis has mostly been restricted to the number of functional operations yet. We show that P-complete problems have no symbolic algorithms using a polylogarithmic number of functional operations, unless P=NC. Moreover, we complement PSPACE-hardness results for problems on OBDD-represented inputs by fixed-parameter intractability results, where the OBDD width serves as the fixed parameter.