94 research outputs found
Symmetry within Solutions
We define the concept of an internal symmetry. This is a symmety within a
solution of a constraint satisfaction problem. We compare this to solution
symmetry, which is a mapping between different solutions of the same problem.
We argue that we may be able to exploit both types of symmetry when finding
solutions. We illustrate the potential of exploiting internal symmetries on two
benchmark domains: Van der Waerden numbers and graceful graphs. By identifying
internal symmetries we are able to extend the state of the art in both cases.Comment: AAAI 2010, Proceedings of Twenty-Fourth AAAI Conference on Artificial
Intelligenc
Constructing Minimal Perfect Hash Functions Using SAT Technology
Minimal perfect hash functions (MPHFs) are used to provide efficient access
to values of large dictionaries (sets of key-value pairs). Discovering new
algorithms for building MPHFs is an area of active research, especially from
the perspective of storage efficiency. The information-theoretic limit for
MPHFs is 1/(ln 2) or roughly 1.44 bits per key. The current best practical
algorithms range between 2 and 4 bits per key. In this article, we propose two
SAT-based constructions of MPHFs. Our first construction yields MPHFs near the
information-theoretic limit. For this construction, current state-of-the-art
SAT solvers can handle instances where the dictionaries contain up to 40
elements, thereby outperforming the existing (brute-force) methods. Our second
construction uses XOR-SAT filters to realize a practical approach with
long-term storage of approximately 1.83 bits per key.Comment: Accepted for AAAI 202
SAT Competition 2018
Peer reviewe
Happy Ending: An Empty Hexagon in Every Set of 30 Points
Satisfiability solving has been used to tackle a range of long-standing open
math problems in recent years. We add another success by solving a geometry
problem that originated a century ago. In the 1930s, Esther Klein's exploration
of unavoidable shapes in planar point sets in general position showed that
every set of five points includes four points in convex position. For a long
time, it was open if an empty hexagon, i.e., six points in convex position
without a point inside, can be avoided. In 2006, Gerken and Nicol\'as
independently proved that the answer is no. We establish the exact bound: Every
30-point set in the plane in general position contains an empty hexagon. Our
key contributions include an effective, compact encoding and a search-space
partitioning strategy enabling linear-time speedups even when using thousands
of cores
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