Graph-Based Algorithms for Boolean Function Manipulation
IEEE Transactions on Computers
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
Symbolic Model Checking
Logic Synthesis and Verification Algorithms
Logic Synthesis and Verification Algorithms
Computers and Intractability: A Guide to the Theory of NP-Completeness
Computers and Intractability: A Guide to the Theory of NP-Completeness
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
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
An experimental study of online scheduling algorithms
Journal of Experimental Algorithmics (JEA)
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
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
On the OBDD Complexity of Threshold Functions and the Variable Ordering Problem
SOFSEM '09 Proceedings of the 35th Conference on Current Trends in Theory and Practice of Computer Science
On the size of (generalized) OBDDs for threshold functions
Information Processing Letters
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Ordered Binary Decision Diagrams (OBDDs) are a data structure for Boolean functions which supports many useful operations. It finds applications in CAD, model checking, and symbolic graph algorithms. We present an application of OBDDs to the problem of scheduling N independent tasks with k different execution times on m identical parallel machines while minimizing the over-all finishing time. In fact, we consider the decision problem if there is a schedule with makespan D. Leung's dynamic programming algorithm solves this problem in time ${\mathcal O}({\rm log} m \cdot N^{2(k-1)})$. In this paper, a symbolic version of Leung's algorithm is presented which uses OBDDs to represent the dynamic programming table T. This heuristical approach solves the scheduling problem by executing ${\mathcal O}(k {\rm log} m {\rm log}(mD))$ operations on OBDDs and is expected to use less time and space than Leung's algorithm if T is large but well-structured. The only known upper bound of ${\mathcal O}((m \cdot D)^{3k+2})$ on its resource usage is trivial. Therefore, we report on experimental studies in which the symbolic method was applied to random scheduling problem instances.