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The Nonapproximability of OBDD Minimization

Detlef Sieling
2002 Information and Computation  
Problem: Compute a variable ordering minimizing the OBDD size for f and .  ...  The reductions seem not to be approximation preserving and we do not know of any nonapproximability result for Optimal Linear Arrangement.  ...  I thank Clemens Gröpl and Martin Sauerhoff for fruitful discussions on the results of Section 6.  ... 
doi:10.1006/inco.2001.3076 fatcat:jrcaoveabjcktl3wprrpyw5obm

On the Nonapproximability of Boolean Functions by OBDDs and Read-k-Times Branching Programs

Beate Bollig, Martin Sauerhoff, Ingo Wegener
2002 Information and Computation  
with respect to the uniform distribution by OBDDs, which are the most important type of branching programs in applications. (2) The first truly exponential lower bound on the size of approximating syntactic  ...  This motivates the investigation of the size of the smallest branching program approximating f .  ...  ACKNOWLEDGMENT Thanks to the anonymous referee for many helpful suggestions and to T. S. Jayram for the pointer to the paper of Babai, Hayes, and Kimmel, leading to the simple proof of Lemma 27.  ... 
doi:10.1006/inco.2002.3174 fatcat:5w23ftty6vhvrpfnrwjnsyk6cu

Page 568 of Mathematical Reviews Vol. , Issue 2003A [page]

2003 Mathematical Reviews  
Klaus Meer (DK-SU-CS; Odense) 2003a:68052 68Q17 68Q05 Sieling, Detlef (D-DORT-FI; Dortmund) The nonapproximability of OBDD minimization.  ...  This ordering can be crucial for the size of the resulting OBDD and the computational problem studied in the paper is that of, given a function (by a OBDD), finding the variable ordering that minimizes  ... 

The Complexity of Minimizing FBDDs [chapter]

Detlef Sieling
1999 Lecture Notes in Computer Science  
In this paper it is shown that the existence of polynomial time approximation schemes for optimizing graph orderings or for minimizing FBDDs implies NP ZPP or NP P, respectively, and so such algorithms  ...  Free Binary Decision Diagrams (FBDDs) are a data structure for the representation and manipulation of Boolean functions.  ...  The Complexity of FBDD Minimization We prove the nonapproximability results by a reduction from a variant of the satisfiability problem which we call @ robust 3-SAT-F (@ Rob3SAT-F ).  ... 
doi:10.1007/3-540-48340-3_23 fatcat:hmbdh6p5mvgtxa4bqd4ecr35we

The complexity of minimizing and learning OBDDs and FBDDs

Detlef Sieling
2002 Discrete Applied Mathematics  
Similar hardness results are shown for the related problems of computing minimal size OBDDs and FBDDs that are consistent with a given set of examples.  ...  The latter result implies that size bounded OBDDs and FBDDs are not PAC-learnable unless NP = RP. ?  ...  Acknowledgements I thank Petr Savickà y for drawing my attention to the learnability questions and Ingo Wegener for fruitful discussions on the proofs in this paper.  ... 
doi:10.1016/s0166-218x(01)00324-9 fatcat:ov4qmifrsreblm5ulyb2skga5u

Page 7834 of Mathematical Reviews Vol. , Issue 2003j [page]

2003 Mathematical Reviews  
minimal number n — 1 of iterations.  ...  for s <2/V3, i.e. the length of the first vector of an LLL-basis is within s~"*! times the minimal possible length.  ... 

On the existence of polynomial time approximation schemes for OBDD minimization [chapter]

Detlef Sieling
1998 Lecture Notes in Computer Science  
The size of Ordered Binary Decision Diagrams (OBDDs) is determined by the chosen variable ordering. A poor choice may cause an OBDD to be too large to fit into the available memory.  ...  time approximation algorithm under the assumption ¡ ¢ -hard to compute the size of an OBDD for an optimal variable ordering since the satisfiability problem for OBDDs can be solved in polynomial time  ...  Acknowledgment This work was inspired by presentations and discussions at the GI Research Seminar on proof verification and approximation algorithms in Dagstuhl in April 1997.  ... 
doi:10.1007/bfb0028562 fatcat:b2kyioouczclzitz3lqkeb3fga

On the influence of the variable ordering for algorithmic learning using OBDDs

Matthias Krause, Petr Savický, Ingo Wegener
2005 Information and Computation  
They have OBDDs of linear size for optimal variable orderings. But for all but a small fraction of all variable orderings one needs large size to represent a list of randomly chosen examples.  ...  In this paper, it is shown that, for some functions, it is necessary to develop an algorithm to learn also a good OBDD variable ordering. There are functions with the following properties.  ...  [6] have also investigated the nonapproximability of Boolean functions with respect to various restricted BDD models.  ... 
doi:10.1016/j.ic.2005.05.004 fatcat:zbegq7yojffkpo3xes6afcfe5m

Minimization of decision trees is hard to approximate

Detlef Sieling
2008 Journal of computer and system sciences (Print)  
In these areas it is important to obtain decision trees of small size. The minimization problem for decision trees is known to be NP-hard.  ...  In this paper the problem is shown to be even hard to approximate up to any constant factor under the assumption P = NP.  ...  Acknowledgments I thank Hans Ulrich Simon and the anonymous referees for hints leading to considerable simplifications of the proofs.  ... 
doi:10.1016/j.jcss.2007.06.014 fatcat:zswpvgnsmjaw3ns33mmeelp4n4

Binary decision diagrams in theory and practice

Rolf Drechsler, Detlef Sieling
2001 International Journal on Software Tools for Technology Transfer (STTT)  
This special section comprises six contributed articles on various aspects of the theory and application of DDs.  ...  Finally we outline several applications of BDDs and their extensions and suggest a number of articles and books for those who wish to pursue the topic in more depth.  ...  We would like to thank the reviewers for their comments and suggestions for improvement for all papers of this special section.  ... 
doi:10.1007/s100090100056 fatcat:ktbf6odmevbo3dbrcde67terru

Weighted A∗ search – unifying view and application

Rüdiger Ebendt, Rolf Drechsler
2009 Artificial Intelligence  
The problem of exact or approximate BDD minimization is introduced as a possible new challenge for heuristic search.  ...  Several variants of weighted A * search are applied to problems of BDD minimization and the more classical domains like blocksworld and sliding-tile puzzles.  ...  Finally, we thank Tony Cohn who, after the coordination of the reviewing process, also found the time to make valuable suggestions to further improve the English presentation of the final version.  ... 
doi:10.1016/j.artint.2009.06.004 fatcat:bfxatwfi75fylddhwtzs3hhxue

Computer Aided Design and Test Decision Diagrams - Concepts and Applications (Dagstuhl Seminar 99041)

Bernd Becker, Christoph Meinel, Shin-Ichi Minato, Fabio Somenzi
1999
Minimization and approximation of Binary DDs (BDDs) • Formal verification of sequential circuits with BDD based methods • Extensions beyond Boolean functions to represent and manipulate word-level circuit  ...  The common aim of all researchers is to deepen the understanding of DDs as a data structure, to improve existing techniques and to explore new fields of application.  ...  Nonapproximability Results for OBDD-and FBDD-Minimization Detlef Sieling, Universität Dortmund The variable ordering problem for OBDDs is the problem to compute a variable ordering minimizing the OBDD  ... 
doi:10.4230/dagsemrep.229 fatcat:ak4x5jst6naabklda2x6mrtylm

Minimization of decision trees is hard to approximate

D. Sieling
18th IEEE Annual Conference on Computational Complexity, 2003. Proceedings.  
In these areas it is important to obtain decision trees of small size. The minimization problem for decision trees is known to be NP-hard.  ...  In this paper the problem is shown to be even hard to approximate up to any constant factor under the assumption P = NP.  ...  Acknowledgments I thank Hans Ulrich Simon and the anonymous referees for hints leading to considerable simplifications of the proofs.  ... 
doi:10.1109/ccc.2003.1214412 dblp:conf/coco/Sieling03 fatcat:ptiecr4oqrfdtf7eevihwtmwy4

Page 1929 of Mathematical Reviews Vol. , Issue Index [page]

Mathematical Reviews  
(Christoph Meinel) 2003d:68070 68Q05 (68Q17, 68Q32, 90C60) — The nonapproximability of OBDD minimization. (English summary) /nform. and Comput. 172 (2002), no. 2, 103-138.  ...  (see 2003£:00022) 92C10 (35K 57) Sieling, Detlef The complexity of minimizing and learning OBDDs and FBDDs. (English summary) Discrete Appl. Math. 122 (2002), no. 1-3, 263-282.  ... 

Page 2004 of Mathematical Reviews Vol. , Issue Index [page]

Mathematical Reviews  
., 2003b:81023 Sieg, Wilfried Calculations by man and machine: conceptual analysis. 2003i:03006 Sieling, Detlef The nonapproximability of OBDD minimization.  ...  (English summary) 2003):94046 Woelfel, Philipp New bounds on the OBDD-size of integer multiplication via universal hashing.  ... 
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