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KTH / EECS / TCS / Jakob Nordström / Video seminars

I have moved to the Department of Computer Science (DIKU) at the University of Copenhagen and also have a part-time affiliation with the Department of Computer Science at Lund University. For now, my webpages still reside at KTH, and are being updated here, but this should change during 2020.

Video seminars

The video seminars are the more or less informal seminar series of the Mathematical Insights into Algorithms for Optimization (MIAO) research group started during the spring of 2020.

These are typically fairly low-key events, and are usually announced only locally. In case you want to receive the announcements, please just let us know by sending an e-mail message to jakob.nordstrom@cs.lth.se and we will do our best to keep you in the loop.

Video seminars autumn 2020

  • Friday Oct 9 at 13:15
    Model counting with probabilistic component caching
    (Shubham Sharma and Kuldeep S. Meel, National University of Singapore)

    Given a Boolean formula F, the problem of model counting, also referred to as #SAT, seeks to compute the number of solutions of F. Model counting is a fundamental problem with a wide variety of applications ranging from planning, quantified information flow to probabilistic reasoning and the like. The modern #SAT solvers tend to be either based on static decomposition, dynamic decomposition, or a hybrid of the two. Despite dynamic decomposition based #SAT solvers sharing much of their architecture with SAT solvers, the core design and heuristics of dynamic decomposition-based #SAT solvers has remained constant for over a decade. In this paper, we revisit the architecture of the state-of-the-art dynamic decomposition-based #SAT tool, sharpSAT, and demonstrate that by introducing a new notion of probabilistic component caching and the usage of universal hashing for exact model counting along with the development of several new heuristics can lead to significant performance improvement over state-of-the-art model-counters. In particular, we develop GANAK, a new scalable probabilistic exact model counter that outperforms state-of-the-art exact and approximate model counters for a wide variety of instances.

  • Friday Sep 25 at 13:15
    Manthan: A data-driven approach for Boolean function synthesis
    (Priyanka Golia and Kuldeep S. Meel, National University of Singapore)

    Boolean functional synthesis is a fundamental problem in computer science with wide-ranging applications and has witnessed a surge of interest resulting in progressively improved techniques over the past decade. Despite intense algorithmic development, a large number of problems remain beyond the reach of the current state-of-the-art techniques. Motivated by the progress in machine learning, we propose Manthan, a novel data-driven approach to Boolean functional synthesis. Manthan views functional synthesis as a classification problem, relying on advances in constrained sampling for data generation, and advances in automated reasoning for a novel proof-guided refinement and provable verification. On an extensive and rigorous evaluation over 609 benchmarks, we demonstrate that Manthan significantly improves upon the current state of the art, solving 356 benchmarks in comparison to 280, which is the most solved by a state-of-the-art technique; thereby, we demonstrate an increase of 76 benchmarks over the current state of the art. The significant performance improvements, along with our detailed analysis, highlights several interesting avenues of future work at the intersection of machine learning, constrained sampling, and automated reasoning.

  • Friday Aug 28 at 13:15
    Tuning Sat4j PB solvers for decision problems
    (Romain Wallon, Université d'Artois)

    During the last decades, many improvements in CDCL SAT solvers have made possible to solve efficiently large problems containing millions of variables and clauses. Despite this practical efficiency, some instances remain out of reach for such solvers. This is particularly true when the input formula requires an exponential size refutation proof in the resolution proof system (as for pigeonhole formulae). This observation motivated the development of another kind of solvers, known as pseudo-Boolean (PB) solvers. These solvers take as inputs a conjunction of PB constraints (integral linear inequations over Boolean variables) and benefit from the cutting planes proof system, which is (in theory) stronger than the resolution proof system. To implement this proof system, current PB solvers follow the direction of modern SAT solvers, by implementing a conflict analysis procedure relying on the application of cutting planes rules. However, adapting the CDCL architecture to take into account PB constraints is not as straightforward as it may look. In particular, many CDCL invariants and properties do not hold anymore as long as PB constraints are considered. While some of them may be safely ignored (e.g., when they affect the decision heuristic, the deletion strategy or the restart policy), some others must be fixed to ensure the soundness of the solver (e.g., by ensuring to preserve the conflict during its analysis).

    In this talk, we will give an overview of the main differences between PB solving and classical SAT solving, and present different approaches that have been designed to take these differences into account to extend the CDCL architecture to PB problems. We will in particular discuss the pros and cons of these approaches, and we will explain how they can be enhanced to improve the practical performance of PB solvers.

  • Friday Aug 21 at 10:15
    Using proofs to analyze SAT solvers
    (Janne Kokkala, Lund University and University of Copenhagen)

    The main idea of this seminar is to give an overview of what one can ask and what one can learn about SAT solvers when analyzing the proof to estimate what part of the work was useful. I will start by giving a 17-ish minute alpha test run for my presentation for our CP paper [1]. After that, I will discuss earlier works that use the same or a similar idea for general insights [2], analyzing VSIDS usefulness [3], and clause exchange for parallel solvers [4,5]. To conclude, we can discuss how this approach could be used for pseudo-Boolean solvers.

    [1] J. I. Kokkala, J. Nordström. Using Resolution Proofs to Analyse CDCL SAT solvers.
    [2] L. Simon. Post Mortem Analysis of SAT Solver Proofs.
    [3] S. Malik, V. Ying. On the efficiency of the VSIDS decision heuristic. (Workshop presentation.)
    [4] G. Audemard, L. Simon. Lazy clause exchange policy for parallel SAT solvers.
    [5] G. Katsirelos, A. Sabharwal, H. Samulowitz, L. Simon. Resolution and parallelizability: Barriers to the efficient parallelization of SAT solvers.

  • Wednesday Aug 19 at 13:15
    On computational aspects of the antibandwidth problem
    (Markus Sinnl, Johannes Kepler University Linz)

    In this talk, we consider the antibandwidth problem, also known as dual bandwidth problem, separation problem and maximum differential coloring problem. Given a labeled graph (i.e., a numbering of the vertices of a graph), the antibandwidth of a node is defined as the minimum absolute difference of its labeling to the labeling of all its adjacent vertices. The goal in the antibandwidth problem is to find a labeling maximizing the antibandwidth. The problem is NP-hard in general graphs and has applications in diverse areas like scheduling, radio frequency assignment, obnoxious facility location and map-coloring.

    There has been much work on deriving theoretical bounds for the problem and also in the design of metaheuristics in recent years. However, the optimality gaps between the best known solution values and reported upper bounds for the HarwellBoeing Matrix-instances, which are the commonly used benchmark instances for this problem, were often very large (e.g., up to 577%).

    We present new mixed-integer programming approaches for the problem, including one approach, which does not directly formulate the problem as optimization problem, but as a series of feasibility problems. We also discuss how these feasibility problems can be encoded with various SAT-encodings, including a new and specialised encoding which exploits a certain staircase-structure occuring in the problem formulation. We present computational results for all the algorithms, including a comparison of the MIP and SAT-approaches. Our developed approaches allow to find the proven optimal solution for eight instances from literature, where the optimal solution was unknown and also provide reduced gaps for eleven additional instances, including improved solution values for seven instances, the largest optimality gap is now 46%. Instances based on the problem were submitted to the SAT Competition 2020.

Video seminars spring 2020

  • Wednesday Jul 15 at 15:00
    Naïve algorithm selection for SAT solving
    (Stephan Gocht, Lund University and University of Copenhagen)

    Although solving propositional formulas is an NP-complete problem, state-of-the-art SAT solvers are able to solve formulas with millions of variables. To obtain good performance it is necessary to configure parameters for heuristic decisions. However, there is no single parameter configuration that is perfect for all formulas, and choosing the parameters is a difficult task. The standard approach is to evaluate different configurations on some formulas and to choose the single configuration, that performs best overall. This configuration, which is called single best solver, is then used to solve new unseen formulas. In this paper we demonstrate how random forests can be used to choose a configuration dynamically based on simple features of the formula. The evaluation shows that our approach is able to outperform the single best solver on formulas that are similar to the training set, but not on formulas from completely new domains.

  • Friday Jun 26 at 10:00
    Behind the scenes of chronological CDCL
    (Sibylle Möhle and Armin Biere, Johannes Kepler University Linz)

    Combining conflict-driven clause learning (CDCL) with chronological backtracking is challenging: Multiple invariants considered crucial in modern SAT solvers are violated, if after conflict analysis the solver does not jump to the assertion level but to a higher decision level instead. In their SAT'18 paper "Chronological Backtracking", Alexander Nadel and Vadim Ryvchim provide a fix to this issue. Moreover, their SAT solver implementing chronological backtracking won the main track of the SAT Competition 2018. In our SAT'19 paper, "Backing Backtracking", we present a formalization and generalization of this method. We prove its correctness and provide an independent implementation.

    In this seminar, we demonstrate the working of chronological CDCL by means of an example. In this example, after a conflict the conflicting clause contains only one literal at conflict level. It is therefore used as a reason for backtracking, thus saving the effort of conflict analysis. We further show which invariants are violated and present new ones followed by a discussion of the rules of our formal framework. We also shed light onto implementation details, including those which are not mentioned in our SAT'19 paper.

  • Monday Jun 22 at 13:30
    McSplit: A partitioning algorithm for maximum common subgraph problems
    (Ciaran McCreesh and James Trimble, University of Glasgow)

    We will give a short introduction to McSplit, an algorithm for the maximum common (connected) subgraph problem coauthored with Patrick Prosser and presented at IJCAI 2017. McSplit resembles a forward-checking constraint programming algorithm, but uses a partitioning data structure to store domains which greatly reduces memory use and time per search node. We will also present our recent work with Stephan Gocht and Jakob Nordström on adding proof logging to the algorithm, turning McSplit into a certifying algorithm whose outputs can be independently verified.

  • Thursday Jun 18 at 20:30
    A pseudo-Boolean approach to nonlinear verification
    (Vincent Liew, University of Washington)

    We discuss some new experimental results showing the promise of using pseudo-Boolean solvers, rather than SAT solvers, to verify bit-vector problems containing multiplication. We use this approach to efficiently verify the commutativity of a multiplier output bit by output bit. We also give some examples of simple bit-vector inequalities where the pseudo-Boolean approach significantly outperformed SAT solvers and even bit-vector solvers. Finally, we give some of our observations on the strengths and weaknesses of different methods of conflict analysis used by pseudo-Boolean solvers.

  • Friday May 8 at 13:15
    Pseudo-Boolean solvers for answer set programming
    (Bart Bogaerts, Vrije Universiteit Brussel)

    Answer set programming (ASP) is a well-established knowledge representation formalism. Most ASP solvers are based on (extensions of) technology from Boolean satisfiability solving. While these solvers have shown to be very successful in many practical applications, their strength is limited by their underlying proof system, resolution. In this research, we present a new tool LP2PB that translates ASP programs into pseudo-Boolean theories, for which solvers based on the (stronger) cutting plane proof system exist. We evaluate our tool, and the potential of cutting-plane-based solving for ASP on traditional ASP benchmarks as well as benchmarks from pseudo-Boolean solving. Our results are mixed: overall, traditional ASP solvers still outperform our translational approach, but several benchmark families are identified where the balance shifts the other way, thereby suggesting that further investigation into a stronger proof system for ASP is valuable.

Published by: Jakob Nordström <jakobn~at-sign~kth~dot~se>
Updated 2020-09-21