Complexity Theoretical Results on Partitioned (Nondeterministic) Binary Decision Diagrams

Bollig, Beate; Wegener, Ingo

doi:10.1007/s002240000128

Cited by 20 publications

(7 citation statements)

References 15 publications

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“…There is a range of varieties. Some algorithms complete in a linear time relative to the input size; others complete in a time that is quadratic O(n 2 ); others complete in an exponential or worse time; and others stop [31].…”

Section: End B the Complexity Of The Sequential Algorithm Of The Tops...mentioning

confidence: 99%

New Distributed-TOPSIS Approach for Multi-Criteria Decision-Making Problems in a Big Data Context

Lamrini

Abounaima

Alaoui

2022

Preprint

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Nowadays, the online environment is extra information-rich and allows companies to offer and receive more and more options and opportunities in multiple areas. Thus, decision-makers have abundantly available alternatives to choose from the best one or rank from the most to the least preferred. However, in the multicriteria decision-making field, most tools support a limited number of alternatives with as narrow criteria as possible. Decision-makers are forced to apply a screening or filtering method to reduce the size of the problem, which will slow down the process and eliminate some potential alternatives from the rest of the decision-making process. Implementing MCDM methods in high-performance parallel and distributed computing environments becomes crucial to ensure the scalability of multicriteria decision-making solutions in Big Data contexts, where one can consider a vast number of alternatives, each being described on the basis of a number of criteria. In this context, we consider TOPSIS one of the most widely used MCDM methods. We present a parallel implementation of TOPSIS based on the MapReduce paradigm. This solution will reduce the response time of the decision-making process and facilitate the analysis of the robustness and sensitivity of the method in a high-dimension problem at a reasonable response time. Three multicriteria analysis problems were evaluated to show the proposed approach's computational efficiency and performance. All experiments are carried out within GCP's Dataproc, a service allowing the execution of Apache Hadoop and Spark tasks in Google Cloud. The results of the tests obtained are very significant and promising.

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Section: End B the Complexity Of The Sequential Algorithm Of The Tops...mentioning

confidence: 99%

New Distributed-TOPSIS Approach for Multi-Criteria Decision-Making Problems in a Big Data Context

Lamrini

Abounaima

Alaoui

2022

Preprint

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“…A similar function is considered in a paper of Bollig & Wegener (1999). The function SIP n is based on a well known technique for constructing functions which are hard for OBDDs (cf.…”

Section: Lower Bounds For Randomized Kobddsmentioning

confidence: 99%

On the size of randomized OBDDs and read-once branching programs for k -stable functions

Sauerhoff¹

2001

Computational Complexity

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In this paper, a simple technique which unifies the known approaches for proving lower bound results on the size of deterministic, nondeterministic, and randomized OBDDs and kOBDDs is described.As an application of this technique, a generic lower bound on the size of randomized OBDDs with bounded error is established for a class of functions which has been studied in the literature on branching programs for a long time. These functions have been called "k-stable" by Jukna. It follows that several standard functions are not contained in the analog of the class BPP for OBDDs. Furthermore, exponential lower bounds on the size of randomized kOBDDs are presented. It is well known that k-stable functions with large k are hard for deterministic read-once branching programs. This is no longer true in the randomized case. It is shown here that a certain k-stable function due to Jukna, Razborov, Savický, and Wegener has randomized branching programs of polynomial size, even with zero error. It follows that P ZPP ∩ NP ∩ coNP for the analogs of these classes defined in terms of the size of read-once branching programs.

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“…In this paper, we study the ordered binary decision diagram (OBDD) representations of Boolean functions given as propositional formulas in conjunctive normal form (CNF). In contrast to other variants of binary decision diagrams, equivalence of OBDDs can be decided in polynomial time, a crucial feature for basic applications in the areas of verification and synthesis [4].…”

Section: Introductionmentioning

confidence: 99%

On Compiling Structured CNFs to OBDDs

Bova

Slivovsky

2015

Lecture Notes in Computer Science

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We present new results on the size of OBDD representations of structurally characterized classes of CNF formulas. First, we identify a natural sufficient condition, which we call the few subterms property, for a class of CNFs to have polynomial OBDD size; we then prove that CNFs whose incidence graphs are variable convex have few subterms (and hence have polynomial OBDD size), and observe that the few subterms property also explains the known fact that classes of CNFs of bounded treewidth have polynomial OBDD size. Second, we prove an exponential lower bound on the OBDD size of a family of CNF classes with incidence graphs of bounded degree, exploiting the combinatorial properties of expander graphs.

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Complexity Theoretical Results on Partitioned (Nondeterministic) Binary Decision Diagrams

Cited by 20 publications

References 15 publications

New Distributed-TOPSIS Approach for Multi-Criteria Decision-Making Problems in a Big Data Context

New Distributed-TOPSIS Approach for Multi-Criteria Decision-Making Problems in a Big Data Context

On the size of randomized OBDDs and read-once branching programs for k -stable functions

On Compiling Structured CNFs to OBDDs

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