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 lowkey events, and are usually announced
only locally. In case you want to receive the announcements, please
just let us know by sending an email message to
jakob.nordstrom@cs.lth.se and we will do our best to keep you in the
loop.
Video seminars autumn 2020

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 NPhard
in general graphs and has applications in diverse areas like
scheduling, radio frequency assignment, obnoxious facility
location and mapcoloring.
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 Matrixinstances, which are the commonly used
benchmark instances for this problem, were often very large
(e.g., up to 577%).
We present new mixedinteger 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 SATencodings, including
a new and specialised encoding which exploits a certain
staircasestructure occuring in the problem formulation. We
present computational results for all the algorithms,
including a comparison of the MIP and SATapproaches. 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 NPcomplete
problem, stateoftheart 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 conflictdriven 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 forwardchecking 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 pseudoBoolean approach to nonlinear verification
(Vincent Liew,
University of Washington)
We discuss some new experimental results showing the promise
of using pseudoBoolean solvers, rather than SAT solvers, to
verify bitvector 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 bitvector inequalities where the pseudoBoolean
approach significantly outperformed SAT solvers and even
bitvector solvers. Finally, we give some of our observations on
the strengths and weaknesses of different methods of conflict
analysis used by pseudoBoolean solvers.

Friday May 8 at 13:15
PseudoBoolean solvers for answer set programming
(Bart Bogaerts, Vrije Universiteit Brussel)
Answer set programming (ASP) is a wellestablished 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
pseudoBoolean theories, for which solvers based on the
(stronger) cutting plane proof system exist. We evaluate our
tool, and the potential of cuttingplanebased solving for ASP
on traditional ASP benchmarks as well as benchmarks from
pseudoBoolean 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.
