pseudo-Boolean Optimization Research Articles

A Hypergraph-Based Reduction for Higher-Order Binary Markov Random Fields.

Higher-order Markov Random Fields, which can capture important properties of natural images, have become increasingly important in computer vision. While graph cuts work well for first-order MRF's, until recently they have rarely been effective for higher-order MRF's. Ishikawa's graph cut technique [1], [2] shows great promise for many higher-order MRF's. His method transforms an arbitrary higher-order MRF with binary labels into a first-order one with the same minima. If all the terms are submodular the exact solution can be easily found; otherwise, pseudoboolean optimization techniques can produce an optimal labeling for a subset of the variables. We present a new transformation with better performance than [1], [2], both theoretically and experimentally. While [1], [2] transforms each higher-order term independently, we use the underlying hypergraph structure of the MRF to transform a group of terms at once. For n binary variables, each of which appears in terms with k other variables, at worst we produce n non-submodular terms, while [1], [2] produces O(nk). We identify a local completeness property under which our method perform even better, and show that under certain assumptions several important vision problems (including common variants of fusion moves) have this property. We show experimentally that our method produces smaller weight of non-submodular edges, and that this metric is directly related to the effectiveness of QPBO [3]. Running on the same field of experts dataset used in [1], [2] we optimally label significantly more variables (96 versus 80 percent) and converge more rapidly to a lower energy. Preliminary experiments suggest that some other higher-order MRF's used in stereo [4] and segmentation [5] are also locally complete and would thus benefit from our work.

A Multilevel Pseudo-Boolean Satisfiability-Based Approach for Segmented Channel Routing

The segmented channel routing problem is fundamental to the routing of row-based field programmable gate arrays (FPGAs) and is proven to be nondeterministic polynomial time (NP) complete. In this paper, we capitalize on the compelling advancements in satisfiability (SAT) solvers to propose a multilevel pseudo-Boolean SAT-based approach. We construct several levels of hierarchy amongst the nets and the routing problem of each level is formulated as a pseudo-Boolean optimization (PBO) problem. Moreover, an optimization technique of reducing the number of variables in PBO problems is described to improve the scalability of the proposed method. Similar to the SAT-based routing, the unroutability of a given circuit can be proved by the approach. Experimental results show that the proposed method compares very favorably with existing algorithms and achieves the best convergence rate.

NestDE: generic parameters tuning for automatic story segmentation

Parameters tuning is a crucial task in automatic story segmentation. For most previous story segmentation methods, however, the parameters were simply derived from empirical tuning, which may indeed harm the fairness of the evaluation, or even misguide the conclusion. In this paper, we present a general parameters tuning approach, namely nested differential evolution. As a practical general-purpose parameters tuner, our approach itself is parameters-robust and is generic enough to optimize the most usual types of parameters for the given corpus and evaluation criterion. Besides, our approach is able to cooperate with empirical tuning and jointly produce better parameters based on the prior knowledge of experienced users. Extensive experiments on synthetic challenging quadratic pseudo-Boolean optimization and real-world story segmentation tasks validate the superior performance of our approach over traditional empirical tuning and other generic optimizers, such as simulated annealing and classical differential evolution.

Video Object Co-Segmentation via Subspace Clustering and Quadratic Pseudo-Boolean Optimization in an MRF Framework

Multiple videos may share a common foreground object, for instance a family member in home videos, or a leading role in various clips of a movie or TV series. In this paper, we present a novel method for co-segmenting the common foreground object from a group of video sequences. The issue was seldom touched on in the literature. Starting from over-segmentation of each video into Temporal Superpixels (TSPs), we first propose a new subspace clustering algorithm which segments the videos into consistent spatio-temporal regions with multiple classes, such that the common foreground has consistent labels across different videos. The subspace clustering algorithm exploits the fact that across different videos the common foreground shares similar appearance features, while motions can be used to better differentiate regions within each video, making accurate extraction of object boundaries easier. We further formulate video object co-segmentation as a Markov Random Field (MRF) model which imposes the constraint of foreground model automatically computed or specified with little user effort. The Quadratic Pseudo-Boolean Optimization (QPBO) is used to generate the results. Experiments show that this video co-segmentation framework can achieve good quality foreground extraction results without user interaction for those videos with unrelated background, and with only moderate user interaction for those videos with similar background. Comparisons with previous work also show the superiority of our approach.

General Upper Bounds on the Runtime of Parallel Evolutionary Algorithms*

We present a general method for analyzing the runtime of parallel evolutionary algorithms with spatially structured populations. Based on the fitness-level method, it yields upper bounds on the expected parallel runtime. This allows for a rigorous estimate of the speedup gained by parallelization. Tailored results are given for common migration topologies: ring graphs, torus graphs, hypercubes, and the complete graph. Example applications for pseudo-Boolean optimization show that our method is easy to apply and that it gives powerful results. In our examples the performance guarantees improve with the density of the topology. Surprisingly, even sparse topologies such as ring graphs lead to a significant speedup for many functions while not increasing the total number of function evaluations by more than a constant factor. We also identify which number of processors lead to the best guaranteed speedups, thus giving hints on how to parameterize parallel evolutionary algorithms.

Inferring phylogenetic trees using pseudo-Boolean optimization

Phylogenetic inference concerns the construction of the most probable tree of evolution, taking into account the knowledge about organisms we have at our disposal. There are various inference methods for building a phylogenetic tree, each with its set of assumptions about what can happen in Nature. Assumptions limit the expressiveness of the methods, but are necessary for making them viable to use. More recently, computational methods are being used to validate results obtained from manual methods. Computational methods allow to address problems that require the analysis of larger sets of data in order to construct more complete phylogenies.In this paper we propose the use of Pseudo-Boolean Optimization PBO, a well known extension of Propositional Satisfiability SAT, in order to solve the Maximum Compatibility MC problem. Assuming that each organism is associated with a set of characteristics, the goal in the MC problem is to find a phylogenetic tree such that the maximum number of characteristics are compatible. Our contribution is a set of new PBO formulations that improve on the performance of the state of the art tool. Comparative results, using real and generated instances, show that the proposed implementations allow the resolution of problem instances with twice the size of the state of the art implementation.

Worst-Case Estimation for Data-Dependent Timing Jitter and Amplitude Noise in High-Speed Differential Link

Differential signaling has been widely used in high-speed interconnects. Signal integrity issues, such as inter-symbol interference (ISI) and crosstalk between the differential pair, however, still cause significant timing jitter and amplitude noise and heavily limit the performance of the differential link. The pre-emphasis filter is commonly used to reduce ISI but may potentially change the crosstalk behavior. In this paper, we first propose formula-based jitter and noise models considering the combined effect of ISI, crosstalk, and pre-emphasis filter. With the same set of input patterns, experiment shows our models achieve within 5% difference compared with SPICE simulation. By utilizing these formula-based models, we then develop algorithms to directly find out the input patterns for worst-case jitter and worst-case amplitude noise through pseudo-Boolean optimization (PBO) and mathematical programming. In addition, a heuristic algorithm is proposed to further reduce runtime. Experiments show our algorithms obtain more reliable worst-case jitter and noise compared with pseudorandom bit sequences simulation and, meanwhile, reduce runtime by 25× when using a general PBO solver and by 150× when using our proposed heuristic algorithm.

Team Theory and Person-by-Person Optimization with Binary Decisions

In this paper, we extend the notion of person-by-person (pbp) optimization to binary decision spaces. The novelty of our approach is the adaptation to a dynamic team context of notions borrowed from the pseudo-boolean optimization field as completely local-global or unimodal functions and submodularity. We also generalize the concept of pbp optimization to the case where groups of $m$ decisions makers make joint decisions sequentially, which we refer to as $m$b$m$ optimization. The main contribution is a description of sufficient conditions, verifiable in polynomial time, under which a pbp or an $m$b$m$ optimization algorithm converges to the team-optimum. As a second contribution, we present a local and greedy algorithm characterized by approximate decision strategies (i.e., strategies based on a local state vector) that return the same decisions as in the complete information framework (where strategies are based on full state vector). As a last contribution, we also show that there exists a subclass of submodular team problems, recognizable in polynomial time, for which the pbp optimization converges for at least an opportune initialization of the algorithm.

Boolean lexicographic optimization: algorithms & applications

Multi-Objective Combinatorial Optimization (MOCO) problems find a wide range of practical application problems, some of which involving Boolean variables and constraints. This paper develops and evaluates algorithms for solving MOCO problems, defined on Boolean domains, and where the optimality criterion is lexicographic. The proposed algorithms build on existing algorithms for either Maximum Satisfiability (MaxSAT), Pseudo-Boolean Optimization (PBO), or Integer Linear Programming (ILP). Experimental results, obtained on problem instances from haplotyping with pedigrees and software package dependencies, show that the proposed algorithms can provide significant performance gains over state of the art MaxSAT, PBO and ILP algorithms. Finally, the paper also shows that lexicographic optimization conditions are observed in the majority of the problem instances from the MaxSAT evaluations, motivating the development of dedicated algorithms that can exploit lexicographic optimization conditions in general MaxSAT problem instances.

Markov random field based phase demodulation of interferometric images

We present a novel method to solve the sign ambiguity for phase demodulation from a single interferometric image that possibly contains closed fringes. The problem is formulated in a Markov random field (MRF) energy minimization framework with the assumption of phase gradient orientation continuity. The binary pairwise objective function is non-submodular and therefore its minimization is an NP-hard problem, for which we devise a multigrid hierarchy of quadratic pseudoboolean optimization problems that can be improved iteratively to approximate the optimal solution. We name the method MSARI algorithm, for Markov based sign ambiguity resolution in interferometry. Compared with traditional path-following phase demodulation methods, the new approach does not require any heuristic scanning strategy, is not subject to the propagation of error, and the extension to three dimensional fringe patterns is straightforward. A set of experiments with synthetic data and real prelens tear film interferometric images of the human eye demonstrate the effectiveness and robustness of the proposed algorithm as compared with existing state-of-the-art phase demodulation methods.

Optimal Feature Matching for 3D Reconstruction by Combination of Global and Local Information

Abstract For feature matching in 3D computer vision, there are two main kinds of methods, i.e. global-based and local-based algorithms. Although both have achieved some useful results, they still have own disadvantages. This paper proposes a novel method which combines the global and local information as much as possible so that it can take both advantages. A series of sub-pixel window correlation method is employed with the guidance of fronto-parallel result to produce some local results. These local results are then repeatedly merged by quadratic pseudo-boolean optimization under the guidance of global information. After several sub-pixel local optimizations, the error rates at high resolution are tremendously reduced. When combining the global and local traits together, the third step optimization can both reduce the low resolution error as well as keep high-accuracy resolution error low. Compared with other existing algorithms, the proposed approach performs well when the scene is comprised with plana...

A Novel SAT-Based Approach to the Task Graph Cost-Optimal Scheduling Problem

The task graph cost-optimal scheduling problem consists in scheduling a certain number of interdependent tasks onto a set of heterogeneous processors (characterized by idle and running rates per time unit), minimizing the cost of the entire process. This paper provides a novel formulation for this scheduling puzzle, in which an optimal solution is computed through a sequence of binate covering problems, hinged within a bounded model checking paradigm. In this approach, each covering instance, providing a min-cost trace for a given schedule depth, can be solved with several strategies, resorting to minimum-cost satisfiability solvers or pseudo-Boolean optimization tools. Unfortunately, all direct resolution methods show very low efficiency and scalability. As a consequence, we introduce a specialized method to solve the same sequence of problems, based on a traditional all-solution SAT solver. This approach follows the “circuit cofactoring” strategy, as it exploits a powerful technique to capture a large set of solutions for any new SAT counter-example. The overall method is completed with a branch-and-bound heuristic which evaluates lower and upper bounds of the schedule length, to reduce the state space that has to be visited. Our results show that the proposed strategy significantly improves the blind binate covering schema, and it outperforms general purpose state-of-the-art tools.

Haplotype Inference by Pure Parsimony: A Survey

Given a set of genotypes from a population, the process of recovering the haplotypes that explain the genotypes is called haplotype inference. The haplotype inference problem under the assumption of pure parsimony consists in finding the smallest number of haplotypes that explain a given set of genotypes. This problem is NP-hard. The original formulations for solving the Haplotype Inference by Pure Parsimony (HIPP) problem were based on integer linear programming and branch-and-bound techniques. More recently, solutions based on Boolean satisfiability, pseudo-Boolean optimization, and answer set programming have been shown to be remarkably more efficient. HIPP can now be regarded as a feasible approach for haplotype inference, which can be competitive with other different approaches. This article provides an overview of the methods for solving the HIPP problem, including preprocessing, bounding techniques, and heuristic approaches. The article also presents an empirical evaluation of exact HIPP solvers on a comprehensive set of synthetic and real problem instances. Moreover, the bounding techniques to the exact problem are evaluated. The final section compares and discusses the HIPP approach with a well-established statistical method that represents the reference algorithm for this problem.

Using DRL* relaxations for quadratically constrained pseudoboolean optimization: application to robust Min-Cut

In this work we focus on solving quadratically constrained pseudoboolean optimization problems with quadratic objective as mixed integer linear programs. The standard mixed integer linear formulation of such problems is strengthened using valid inequalities derived from solving Reformulation-Linearization relaxation called partial DRL* relaxation. The proposed PDRL* relaxation features block-decomposable structure which are exploited to improve computational efficiency. We present computational results obtained with the rank 2 PDRL*, showing that the proposed mixed integer linear formulation gives rise to significant reduction factors (typically more than 1000) in the size of the branch and bound trees on instances of robust minimum cut problem with weight constraints.

Comparison of PBO solvers in a dependency solving domain

Linux package managers have to deal with dependencies and conflicts of packages required to be installed by the user. As an NP-complete problem, this is a hard task to solve. In this context, several approaches have been pursued. Apt-pbo is a package manager based on the apt project that encodes the dependency solving problem as a pseudo-Boolean optimization (PBO) problem. This paper compares different PBO solvers and their effectiveness on solving the dependency solving problem.

DFT and Minimum Leakage Pattern Generation for Static Power Reduction During Test and Burn-In

This paper presents a design for testability and minimum leakage pattern generation technique to reduce static power during test and burn-in for nanometer technologies. This technique transforms the minimum leakage pattern generation problem into a pseudo-Boolean optimization (PBO) problem. Nonlinear objective functions of leakage power are approximated by linear ones such that this problem can be solved efficiently by an existing PBO solver. A partitioning-based algorithm is applied for control point insertion and also CPU time reduction. Experimental results on the IEEE ISCAS'89 benchmark circuits using Taiwan Semiconductor Manufacturing Company 90-nm technology show that, for large circuits, the static power is reduced from 8.3% (without partition) to 17.47% (with 64 partitions). Besides, the overall CPU time is reduced from 3600 s (without partition) to 83 s (with 64 partitions). This technique reduces the static power without changing the manufacturing process or library cells.

A fast bioluminescent source localization method based on generalized graph cuts with mouse model validations

Bioluminescence imaging (BLI) makes it possible to elucidate molecular and cellular signatures to better understand the effects of human disease in small animal models in vivo. The unambiguous three-dimensional bioluminescent source information obtained by bioluminescence tomography (BLT) could further facilitate its applications in biomedicine. However, to the best of our knowledge, the existing gradient-type reconstruction methods in BLT are inefficient, and often require a relatively small volume of interest (VOI) for feasible results. In this paper, a fast generalized graph cuts based reconstruction method for BLT is presented, which is to localize the bioluminescent source in heterogeneous mouse tissues via max-flow/min-cut algorithm. Since the original graph cuts theory can only handle graph-representable problem, the quadratic pseudo-boolean optimization is incorporated to make the graph representable and tractable, which is called generalized graph cuts (GGC). The internal light source can be reconstructed from the whole domain, so a priori knowledge of VOI can be avoided in this method. In the simulation validations, the proposed method was validated in a heterogeneous mouse atlas, and the source can be localized reliably and efficiently by GGC; and compared with gradient-type method, the proposed method is about 25-50 times faster. Moreover, the experiments for sensitivity to the measurement errors of tissue optical properties demonstrate that, the reconstruction quality is not much affected by mismatch of parameters. In what follows, in vivo mouse BLT reconstructions further demonstrated the potential and effectiveness of the generalized graph cut based reconstruction method.

Combinatorial Optimization Solutions for the Maximum Quartet Consistency Problem

Phylogenetic analysis is a widely used technique, for example in biology and biomedical sciences. The construction of phylogenies can be computationally hard. A commonly used solution for construction of phylogenies is to start from a set of biological species and relations among those species. This work addresses the case where the relations among species are specified as quartet topologies. Moreover, the problem to be solved consists of computing a phylogeny that satisfies the maximum number of quartet topologies. This is referred to as the Maximum Quartet Consistency (MQC) problem, and represents an NP-hard optimization problem. MQC has been solved both heuristically and exactly. Exact solutions for MQC include those based on Constraint Programming, Answer Set Programming, Pseudo-Boolean Optimization (PBO), and Satisfiability Modulo Theories (SMT). This paper provides a comprehensive overview of the use of PBO and SMT for solving MQC, and builds on recent work in this area. Moreover, the paper provides new insights on how to use SMT for solving optimization problems, by focusing on the concrete case of MQC. The solutions based on PBO and SMT were experimentally compared with other exact solutions. The results show that for instances with small percentage of quartet errors, the models based on SMT can be competitive, whereas for instances with higher number of quartet errors the PBO models are more efficient.

Theorems Supporting r-flip Search for Pseudo-Boolean Optimization

Modern metaheuristic methodologies rely on well defined neighborhood structures and efficient means for evaluating potential moves within these structures. Move mechanisms range in complexity from simple 1-flip procedures where binary variables are “flipped” one at a time, to more expensive, but more powerful, r-flip approaches where “r” variables are simultaneously flipped. These multi-exchange neighborhood search strategies have proven to be effective approaches for solving a variety of combinatorial optimization problems. In this paper, we present a series of theorems based on partial derivatives that can be readily adopted to form the essential part of r-flip heuristic search methods for Pseudo-Boolean optimization. To illustrate the use of these results, we present preliminary results obtained from four simple heuristics designed to solve a set of Max 3-SAT problems.

Haplotype inference with pseudo-Boolean optimization

The fast development of sequencing techniques in the recent past has required an urgent development of efficient and accurate haplotype inference tools. Besides being a crucial issue in genetics, haplotype inference is also a challenging computational problem. Among others, pure parsimony is a viable modeling approach to solve the problem of haplotype inference and also an interesting NP-hard problem in itself. Recently, the introduction of SAT-based methods, including pseudo-Boolean optimization (PBO) methods, has produced very efficient solvers. This paper provides a detailed description of RPoly, a PBO approach for the haplotype inference by pure parsimony (HIPP) problem. Moreover, an extensive evaluation of existent HIPP solvers, on a comprehensive set of instances, confirms that RPoly is currently the most efficient and robust HIPP approach.