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

Compressing Binary Decision Diagrams

The paper introduces a new technique for compressing Binary Decision Diagrams in those cases where random access is not required. Using this technique, compression and decompression can be done in linear time in the size of the BDD and compression will in many cases reduce the size of the BDD to 1-2 bits per node. Empirical results for our compression technique are presented, including comparisons with previously introduced techniques, showing that the new technique dominate on all tested instances.Comment: Full (tech-report) version of ECAI 2008 short pape

Construction of Decision Diagrams for Product Configuration

Knowledge compilation is a well-researched field focused on translating propositional logic formulas into efficient data structures that allow polynomial-time online queries related to the SAT problem. Knowledge compilation techniques can be used to partition product configuration tasks into two distinct phases: fast online processing and slow offline preprocessing. Binary Decision Diagrams (BDDs) are widely studied in this area and provide a graph representation of Boolean formulas. However, BDD construction can be time-consuming, particularly for large instances, as their size grows exponentially with the number of variables. This paper explores methods to improve BDD construction time, including optimizing variable ordering. The evaluation involves applying these techniques to formulas in Rich Conjunctive Normal Form, comparing the results with Sentential Decision Diagrams. The experiments use CAS Software AG benchmarks

Boosting-based Construction of BDDs for Linear Threshold Functions and Its Application to Verification of Neural Networks

Understanding the characteristics of neural networks is important but difficult due to their complex structures and behaviors. Some previous work proposes to transform neural networks into equivalent Boolean expressions and apply verification techniques for characteristics of interest. This approach is promising since rich results of verification techniques for circuits and other Boolean expressions can be readily applied. The bottleneck is the time complexity of the transformation. More precisely, (i) each neuron of the network, i.e., a linear threshold function, is converted to a Binary Decision Diagram (BDD), and (ii) they are further combined into some final form, such as Boolean circuits. For a linear threshold function with $n$ variables, an existing method takes $O(n2^{\frac{n}{2}})$ time to construct an ordered BDD of size $O(2^{\frac{n}{2}})$ consistent with some variable ordering. However, it is non-trivial to choose a variable ordering producing a small BDD among $n!$ candidates. We propose a method to convert a linear threshold function to a specific form of a BDD based on the boosting approach in the machine learning literature. Our method takes $O(2^n \text{poly}(1/\rho))$ time and outputs BDD of size $O(\frac{n^2}{\rho^4}\ln{\frac{1}{\rho}})$, where $\rho$ is the margin of some consistent linear threshold function. Our method does not need to search for good variable orderings and produces a smaller expression when the margin of the linear threshold function is large. More precisely, our method is based on our new boosting algorithm, which is of independent interest. We also propose a method to combine them into the final Boolean expression representing the neural network

Efficient parallel binary decision diagram construction using Cilk

Thesis (S.B. and M.Eng.)--Massachusetts Institute of Technology, Dept. of Electrical Engineering and Computer Science, 2000.Includes bibliographical references (leaves 44-45).by David B. Berman.S.B.and M.Eng

Conformant Planning via Symbolic Model Checking

We tackle the problem of planning in nondeterministic domains, by presenting a new approach to conformant planning. Conformant planning is the problem of finding a sequence of actions that is guaranteed to achieve the goal despite the nondeterminism of the domain. Our approach is based on the representation of the planning domain as a finite state automaton. We use Symbolic Model Checking techniques, in particular Binary Decision Diagrams, to compactly represent and efficiently search the automaton. In this paper we make the following contributions. First, we present a general planning algorithm for conformant planning, which applies to fully nondeterministic domains, with uncertainty in the initial condition and in action effects. The algorithm is based on a breadth-first, backward search, and returns conformant plans of minimal length, if a solution to the planning problem exists, otherwise it terminates concluding that the problem admits no conformant solution. Second, we provide a symbolic representation of the search space based on Binary Decision Diagrams (BDDs), which is the basis for search techniques derived from symbolic model checking. The symbolic representation makes it possible to analyze potentially large sets of states and transitions in a single computation step, thus providing for an efficient implementation. Third, we present CMBP (Conformant Model Based Planner), an efficient implementation of the data structures and algorithm described above, directly based on BDD manipulations, which allows for a compact representation of the search layers and an efficient implementation of the search steps. Finally, we present an experimental comparison of our approach with the state-of-the-art conformant planners CGP, QBFPLAN and GPT. Our analysis includes all the planning problems from the distribution packages of these systems, plus other problems defined to stress a number of specific factors. Our approach appears to be the most effective: CMBP is strictly more expressive than QBFPLAN and CGP and, in all the problems where a comparison is possible, CMBP outperforms its competitors, sometimes by orders of magnitude

NANOCONTROLLER PROGRAM OPTIMIZATION USING ITE DAGS

Kentucky Architecture nanocontrollers employ a bit-serial SIMD-parallel hardware design to execute MIMD control programs. A MIMD program is transformed into equivalent SIMD code by a process called Meta-State Conversion (MSC), which makes heavy use of enable masking to distinguish which code should be executed by each processing element. Both the bit-serial operations and the enable masking imposed on them are expressed in terms of if-then-else (ITE) operations implemented by a 1-of-2 multiplexor, greatly simplifying the hardware. However, it takes a lot of ITEs to implement even a small program fragment. Traditionally, bit-serial SIMD machines had been programmed by expanding a fixed bitserial pattern for each word-level operation. Instead, nanocontrollers can make use of the fact that ITEs are equivalent to the operations in Binary Decision Diagrams (BDDs), and can apply BDD analysis to optimize the ITEs. This thesis proposes and experimentally evaluates a number of techniques for minimizing the complexity of the BDDs, primarily by manipulating normalization ordering constraints. The best method found is a new approach in which a simple set of optimization transformations is followed by normalization using an ordering determined by a Genetic Algorithm (GA)