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Efficient ExternalMemory Data Structures and Applications
, 1996
"... In this thesis we study the Input/Output (I/O) complexity of largescale problems arising e.g. in the areas of database systems, geographic information systems, VLSI design systems and computer graphics, and design I/Oefficient algorithms for them. A general theme in our work is to design I/Oeffic ..."
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Cited by 37 (9 self)
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In this thesis we study the Input/Output (I/O) complexity of largescale problems arising e.g. in the areas of database systems, geographic information systems, VLSI design systems and computer graphics, and design I/Oefficient algorithms for them. A general theme in our work is to design I/Oefficient algorithms through the design of I/Oefficient data structures. One of our philosophies is to try to isolate all the I/O specific parts of an algorithm in the data structures, that is, to try to design I/O algorithms from internal memory algorithms by exchanging the data structures used in internal memory with their external memory counterparts. The results in the thesis include a technique for transforming an internal memory tree data structure into an external data structure which can be used in a batched dynamic setting, that is, a setting where we for example do not require that the result of a search operation is returned immediately. Using this technique we develop batched dynamic external versions of the (onedimensional) rangetree and the segmenttree and we develop an external priority queue. Following our general philosophy we show how these structures can be used in standard internal memory sorting algorithms
Efficient Boolean Manipulation with OBDD's Can be Extended to FBDD's
, 1993
"... OBDD's are the stateoftheart data structure for Boolean function manipulation since basic tasks of Boolean manipulation such as testing equivalence, satisfiability, or tautology, and performing single Boolean synthesis steps can be done efficiently. In the following we show that the efficien ..."
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Cited by 36 (0 self)
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OBDD's are the stateoftheart data structure for Boolean function manipulation since basic tasks of Boolean manipulation such as testing equivalence, satisfiability, or tautology, and performing single Boolean synthesis steps can be done efficiently. In the following we show that the efficient manipulation of OBDD's can be extended to a more general data structure, socalled FBDD's. In detail, the advantages of using FBDD's instead of OBDD's are ffl FBDD's are generally more (sometimes even exponentially more) succinct than OBDD's, ffl FBDD's provide, similarly to OBDD's, canonical representations of Boolean functions, and ffl in terms of FBDD's basic tasks of Boolean manipulation can be performed similarly efficient as in terms of OBDD's. The power of the FBDDconcept is demonstrated by showing that the verification of the benchmark circuit design for the hidden weighted bit function HWB proposed by Bryant can be carried out efficiently in terms of FBDD's while, for princip...
The I/OComplexity of Ordered BinaryDecision Diagram Manipulation
 UNIVERSITY OF AARHUS
, 1995
"... Ordered BinaryDecision Diagrams (OBDD) are the stateoftheart data structure for boolean function manipulation and there exist several software packages for OBDD manipulation. OBDDs have been successfully used to solve problems in e.g. digitalsystems design, verification and testing, in math ..."
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Cited by 22 (15 self)
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Ordered BinaryDecision Diagrams (OBDD) are the stateoftheart data structure for boolean function manipulation and there exist several software packages for OBDD manipulation. OBDDs have been successfully used to solve problems in e.g. digitalsystems design, verification and testing, in mathematical logic, concurrent system design and in artificial intelligence. The OBDDs used in many of these applications quickly get larger than the avaliable main memory and it becomes essential to consider the problem of minimizing the Input/Output (I/O) communication. In this paper we analyze why existing OBDD manipulation algorithms perform poorly in an I/O environment and develop new I/Oefficient algorithms.
Some Heuristics for Generating Treelike FBDD Types
 IEEE Trans. on ComputerAided Design of Integrated Circuits and Systems
, 1996
"... Reduced ordered binary decision diagrams (OBDDs) are nowadays the stateoftheart representation scheme for Boolean functions in Boolean manipulation. Recent results have shown that it is possible to use the more general concept of free binary decision diagrams (FBDDs) without giving up most of the ..."
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Cited by 12 (0 self)
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Reduced ordered binary decision diagrams (OBDDs) are nowadays the stateoftheart representation scheme for Boolean functions in Boolean manipulation. Recent results have shown that it is possible to use the more general concept of free binary decision diagrams (FBDDs) without giving up most of the useful computational properties of OBDDs, but possibly reducing the space requirements considerably. The amount of space reduction depends essentially on the shape of so called FBDDtypes the Boolean manipulation in terms of FBDDs is based on. In this paper we start to propose some heuristics for deriving treelike FBDDtypes from given circuit descriptions. The experimental results we obtained demonstrate clearly that the FBDDapproach is not only of theoretical interest but also of practical usefulness even in the case of using merely such simplestructured treebased FBDD types as produced by the investigated heuristics. Keywords data structures for switching functions, OBDD,...
Efficient OBDDBased Boolean Manipulation in CAD Beyond Current Limits
 in Proceedings of 32nd Design Automation Conference
, 1995
"... We present the concept of TBDD's which considerably enlarges the class of Boolean functions that can be efficiently manipulated in terms of OBDD's. It extends the idea of using domain transformations, which is wellknown in many areas of mathematics, physics, and technical sciences, to the ..."
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Cited by 12 (0 self)
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We present the concept of TBDD's which considerably enlarges the class of Boolean functions that can be efficiently manipulated in terms of OBDD's. It extends the idea of using domain transformations, which is wellknown in many areas of mathematics, physics, and technical sciences, to the context of OBDDbased Boolean function manipulation in CAD: Instead of working with the OBDDrepresentation of a function f , TBDD's allow working with an OBDDrepresentation of a suited cube transformed version of f . Besides of giving some theoretical insights into the new concept, we investigate in some detail cube transformations which are based on complete types. We ffl show that such TBDDrepresentations can be derived similarly as OBDDrepresentations, ffl give evidence of the practical importance of such TBDD's by presenting very smallsize TBDDrepresentations of the hidden weighted bit functions HWBn which were proved to have only very large OBDDrepresentations, and ffl report some pr...
Complexity Theoretical Results for Randomized Branching Programs
, 1998
"... This work is settled in the area of complexity theory for restricted variants of branching programs. Today, branching programs can be considered one of the standard nonuniform models of computation. One reason for their popularity is that they allow to describe computations in an intuitively straigh ..."
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Cited by 8 (7 self)
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This work is settled in the area of complexity theory for restricted variants of branching programs. Today, branching programs can be considered one of the standard nonuniform models of computation. One reason for their popularity is that they allow to describe computations in an intuitively straightforward way and promise to be easier to analyze than the traditional models. In complexity theory, we are mainly interested in upper and lower bounds on the size of branching programs. Although proving superpolynomial lower bounds on the size of general branching programs still remains a challenging open problem, there has been considerable success in the study of lower bound techniques for various restricted variants, most notably perhaps readonce branching programs and OBDDs (ordered binary decision diagrams). Surprisingly, OBDDs have also turned out to be extremely useful in practical applications as a data structure for Boolean functions. So far, research has concentrated on determinis...
⊕OBDDs  a BDD Structure for Probabilistic Verification
 IN PROC. OF THE PRELICS WORKSHOP ON PROBABILISTIC METHODS IN VERIFICATION (PROBMIV'98
, 1998
"... Ordered Binary Decision Diagrams (OBDDs) have already proved useful in the verification of combinational and sequential circuits. Due to limitations of the descriptive power of OBDDs several more general models of Binary Decision Diagrams have been studied. In this paper, ⊕OBDDs  also known as Mod ..."
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Cited by 6 (4 self)
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Ordered Binary Decision Diagrams (OBDDs) have already proved useful in the verification of combinational and sequential circuits. Due to limitations of the descriptive power of OBDDs several more general models of Binary Decision Diagrams have been studied. In this paper, ⊕OBDDs  also known as Mod2OBDDs  in respect to their ability to serve as a tool for combinational verification are considered. Besides the application of ⊕OBDDs, the more general problem of how to exploit the inherent potential of ⊕OBDDs more efficiently is addressed.
A Lower Bound Technique for Nondeterministic GraphDriven ReadOnceBranching Programs and its Applications (Extended Abstract)
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A Unifying Theoretical Background for Some BDDbased Data Structures
, 1994
"... In the paper, we propose a general concept (in what follows denoted by TBDD) for Boolean functions manipulation that is based on cube transformations. The basic idea is to manipulate a Boolean function by converting it by means of a cube transformation into a function that can be efficiently repres ..."
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Cited by 4 (1 self)
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In the paper, we propose a general concept (in what follows denoted by TBDD) for Boolean functions manipulation that is based on cube transformations. The basic idea is to manipulate a Boolean function by converting it by means of a cube transformation into a function that can be efficiently represented and manipulated in terms of ordered binary decision diagrams (OBDD's). We show that the new concept unifies and simplifies known BDDbased data structures considerably, and allows to work in all cases with the simplestructured and wellcomprehended data struture of OBDD's (what is especially important from the point of practical applications.) Further, to give an example how TBDD's open new ways in the search for efficient data structures for Boolean functions, we discuss the data structure of typed kFBDD's.
Variable Orderings For OBDDs, Simulated Annealing, And The Hidden Weighted Bit Function
 University of Dortmund
, 1996
"... Ordered binary decision diagrams (OBDDs) are an efficient graph representation for Boolean functions, if good variable orderings are used. Variable orderings are computed by heuristic algorithms and improved with the simulated annealing approach. New neighborhoods for simulated annealing algorith ..."
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Cited by 3 (0 self)
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Ordered binary decision diagrams (OBDDs) are an efficient graph representation for Boolean functions, if good variable orderings are used. Variable orderings are computed by heuristic algorithms and improved with the simulated annealing approach. New neighborhoods for simulated annealing algorithms are presented. It is investigated how the OBDD size may change in one iteration step for the different neighborhoods. The hidden weighted bit function HWB is a function whose OBDD size depends heavily on the variable ordering although the OBDD size grows exponentially in any case. Variable orderings for HWB are investigated theoretically and experimentally. All known heuristics work badly for HWB, while the new simulated annealing algorithm yields good results for this and other functions. Supported in part by DFG grant We 1066/71. 1 1. INTRODUCTION Ordered binary decision diagrams (OBDDs) are an efficient graph representation (Bryant [3]), if good variable orderings are know...