Exact Computation of Influence Spread by Binary Decision Diagrams

Evaluating influence spread in social networks is a fundamental procedure to estimate the word-of-mouth effect in viral marketing. There are enormous studies about this topic; however, under the standard stochastic cascade models, the exact computation of influence spread is known to be #P-hard. Thus, the existing studies have used Monte-Carlo simulation-based approximations to avoid exact computation. We propose the first algorithm to compute influence spread exactly under the independent cascade model. The algorithm first constructs binary decision diagrams (BDDs) for all possible realizations of influence spread, then computes influence spread by dynamic programming on the constructed BDDs. To construct the BDDs efficiently, we designed a new frontier-based search-type procedure. The constructed BDDs can also be used to solve other influence-spread related problems, such as random sampling without rejection, conditional influence spread evaluation, dynamic probability update, and gradient computation for probability optimization problems. We conducted computational experiments to evaluate the proposed algorithm. The algorithm successfully computed influence spread on real-world networks with a hundred edges in a reasonable time, which is quite impossible by the naive algorithm. We also conducted an experiment to evaluate the accuracy of the Monte-Carlo simulation-based approximation by comparing exact influence spread obtained by the proposed algorithm.Comment: WWW'1

Chain Reduction for Binary and Zero-Suppressed Decision Diagrams

Chain reduction enables reduced ordered binary decision diagrams (BDDs) and zero-suppressed binary decision diagrams (ZDDs) to each take advantage of the others' ability to symbolically represent Boolean functions in compact form. For any Boolean function, its chain-reduced ZDD (CZDD) representation will be no larger than its ZDD representation, and at most twice the size of its BDD representation. The chain-reduced BDD (CBDD) of a function will be no larger than its BDD representation, and at most three times the size of its CZDD representation. Extensions to the standard algorithms for operating on BDDs and ZDDs enable them to operate on the chain-reduced versions. Experimental evaluations on representative benchmarks for encoding word lists, solving combinatorial problems, and operating on digital circuits indicate that chain reduction can provide significant benefits in terms of both memory and execution time

SMTBDD: New Form of BDD for Logic Synthesis

The main purpose of the paper is to suggest a new form of BDD – SMTBDD diagram, methods of obtaining, and its basic features. The idea of using SMTBDD diagram in the process of logic synthesis dedicated to FPGA structures is presented. The creation of SMTBDD diagrams is the result of cutting BDD diagram which is the effect of multiple decomposition. The essence of a proposed decomposition method rests on the way of determining the number of necessary ‘g’ bounded functions on the basis of the content of a root table connected with an appropriate SMTBDD diagram. The article presents the methods of searching non-disjoint decomposition using SMTBDD diagrams. Besides, it analyzes the techniques of choosing cutting levels as far as effective technology mapping is concerned. The paper also discusses the results of the experiments which confirm the efficiency of the analyzed decomposition methods

JINC - A Multi-Threaded Library for Higher-Order Weighted Decision Diagram Manipulation

Ordered Binary Decision Diagrams (OBDDs) have been proven to be an efficient data structure for symbolic algorithms. The efficiency of the symbolic methods de- pends on the underlying OBDD library. Available OBDD libraries are based on the standard concepts and so far only differ in implementation details. This thesis introduces new techniques to increase run-time and space-efficiency of an OBDD library. This thesis introduces the framework of Higher-Order Weighted Decision Diagrams (HOWDDs) to combine the similarities of different OBDD variants. This frame- work pioneers the basis for the new variant Toggling Algebraic Decision Diagrams (TADDs) which has been shown to be a space-efficient HOWDD variant for sym- bolic matrix representation. The concept of HOWDDs has been use to implement the OBDD library JINC. This thesis also analyzes the usage of multi-threading techniques to speed-up OBDD manipulations. A new reordering framework ap- plies the advantages of multi-threading techniques to reordering algorithms. This approach uses an abstraction layer so that the original reordering algorithms are not touched. The challenge that arise from a straight forward algorithm is that the computed-tables and the garbage collection are not as efficient as in a single- threaded environment. We resolve this problem by developing a new multi-operand APPLY algorithm that eliminates the creation of temporary nodes which could occur during computation and thus reduces the need for caching or garbage collection. The HOWDD framework leads to an efficient library design which has been shown to be more efficient than the established OBDD library CUDD. The HOWDD instance TADD reduces the needed number of nodes by factor two compared to ordinary ADDs. The new multi-threading approaches are more efficient than single-threading approaches by several factors. In the case of the new reordering framework the speed- up almost equals the theoretical optimal speed-up. The novel multi-operand APPLY algorithm reduces the memory usage for the n-queens problem by factor 50 which enables the calculation of bigger problem instances compared to the traditional APPLY approach. The new approaches improve the performance and reduce the memory footprint. This leads to the conclusion that applications should be reviewed whether they could benefit from the new multi-threading multi-operand approaches introduced and discussed in this thesis

Combinatorial methods for the evaluation of yield and operational reliability of fault-tolerant systems-on-chip

In this paper we develop combinatorial methods for the evaluation of yield and operational reliability of fault-tolerant systems-on-chip. The method for yield computation assumes that defects are produced according to a model in which defects are lethal and affect given components of the system following a distribution common to all defects; the method for the computation of operational reliability also assumes that the fault-tree function of the system is increasing. The distribution of the number of defects is arbitrary. The methods are based on the formulation of, respectively, the yield and the operational reliability as the probability that a given boolean function with multiple-valued variables has value 1. That probability is computed by analyzing a ROMDD (reduced ordered multiple-value decision diagram) representation of the function. For efficiency reasons, a coded ROBDD (reduced ordered binary decision diagram) representation of the function is built first and, then, that coded ROBDD is transformed into the ROMDD required by the methods. We present numerical experiments showing that the methods are able to cope with quite large systems in moderate CPU times.Postprint (published version

MALL proof equivalence is Logspace-complete, via binary decision diagrams

Proof equivalence in a logic is the problem of deciding whether two proofs are equivalent modulo a set of permutation of rules that reflects the commutative conversions of its cut-elimination procedure. As such, it is related to the question of proofnets: finding canonical representatives of equivalence classes of proofs that have good computational properties. It can also be seen as the word problem for the notion of free category corresponding to the logic. It has been recently shown that proof equivalence in MLL (the multiplicative with units fragment of linear logic) is PSPACE-complete, which rules out any low-complexity notion of proofnet for this particular logic. Since it is another fragment of linear logic for which attempts to define a fully satisfactory low-complexity notion of proofnet have not been successful so far, we study proof equivalence in MALL- (multiplicative-additive without units fragment of linear logic) and discover a situation that is totally different from the MLL case. Indeed, we show that proof equivalence in MALL- corresponds (under AC0 reductions) to equivalence of binary decision diagrams, a data structure widely used to represent and analyze Boolean functions efficiently. We show these two equivalent problems to be LOGSPACE-complete. If this technically leaves open the possibility for a complete solution to the question of proofnets for MALL-, the established relation with binary decision diagrams actually suggests a negative solution to this problem.Comment: in TLCA 201

Biconditional Binary Decision Diagrams: A Novel Canonical Logic Representation Form

In this paper, we present biconditional binary deci- sion diagrams (BBDDs), a novel canonical representation form for Boolean functions. BBDDs are binary decision diagrams where the branching condition, and its associated logic expansion, is biconditional on two variables. Empowered by reduction and ordering rules, BBDDs are remarkably compact and unique for a Boolean function. The interest of such representation form in modern electronic design automation (EDA) is twofold. On the one hand, BBDDs improve the efficiency of traditional EDA tasks based on decision diagrams, especially for arithmetic intensive designs. On the other hand, BBDDs represent the natural and native design abstraction for emerging technologies where the circuit primitive is a comparator, rather than a simple switch. We provide, in this paper, a solid ground for BBDDs by studying their underlying theory and manipulation properties. Thanks to an efficient BBDD software package implementation, we validate 1) speed-up in traditional decision diagrams applications with up to 4.4 gain with respect to other DDs, and 2) improved synthesis of circuits in emerging technologies, with about 32% shorter critical path than state-of-art synthesis techniques