58,490 research outputs found
When Gravity Fails: Local Search Topology
Local search algorithms for combinatorial search problems frequently
encounter a sequence of states in which it is impossible to improve the value
of the objective function; moves through these regions, called plateau moves,
dominate the time spent in local search. We analyze and characterize plateaus
for three different classes of randomly generated Boolean Satisfiability
problems. We identify several interesting features of plateaus that impact the
performance of local search algorithms. We show that local minima tend to be
small but occasionally may be very large. We also show that local minima can be
escaped without unsatisfying a large number of clauses, but that systematically
searching for an escape route may be computationally expensive if the local
minimum is large. We show that plateaus with exits, called benches, tend to be
much larger than minima, and that some benches have very few exit states which
local search can use to escape. We show that the solutions (i.e., global
minima) of randomly generated problem instances form clusters, which behave
similarly to local minima. We revisit several enhancements of local search
algorithms and explain their performance in light of our results. Finally we
discuss strategies for creating the next generation of local search algorithms.Comment: See http://www.jair.org/ for any accompanying file
Theory and Techniques for Synthesizing a Family of Graph Algorithms
Although Breadth-First Search (BFS) has several advantages over Depth-First
Search (DFS) its prohibitive space requirements have meant that algorithm
designers often pass it over in favor of DFS. To address this shortcoming, we
introduce a theory of Efficient BFS (EBFS) along with a simple recursive
program schema for carrying out the search. The theory is based on dominance
relations, a long standing technique from the field of search algorithms. We
show how the theory can be used to systematically derive solutions to two graph
algorithms, namely the Single Source Shortest Path problem and the Minimum
Spanning Tree problem. The solutions are found by making small systematic
changes to the derivation, revealing the connections between the two problems
which are often obscured in textbook presentations of them.Comment: In Proceedings SYNT 2012, arXiv:1207.055
Computing Storyline Visualizations with Few Block Crossings
Storyline visualizations show the structure of a story, by depicting the
interactions of the characters over time. Each character is represented by an
x-monotone curve from left to right, and a meeting is represented by having the
curves of the participating characters run close together for some time. There
have been various approaches to drawing storyline visualizations in an
automated way. In order to keep the visual complexity low, rather than
minimizing pairwise crossings of curves, we count block crossings, that is,
pairs of intersecting bundles of lines.
Partly inspired by the ILP-based approach of Gronemann et al. [GD 2016] for
minimizing the number of pairwise crossings, we model the problem as a
satisfiability problem (since the straightforward ILP formulation becomes more
complicated and harder to solve). Having restricted ourselves to a decision
problem, we can apply powerful SAT solvers to find optimal drawings in
reasonable time. We compare this SAT-based approach with two exact algorithms
for block crossing minimization, using both the benchmark instances of
Gronemann et al. and random instances. We show that the SAT approach is
suitable for real-world instances and identify cases where the other algorithms
are preferable.Comment: Appears in the Proceedings of the 25th International Symposium on
Graph Drawing and Network Visualization (GD 2017
Verification of Sequential Circuits by Tests-As-Proofs Paradigm
We introduce an algorithm for detection of bugs in sequential circuits. This
algorithm is incomplete i.e. its failure to find a bug breaking a property P
does not imply that P holds. The appeal of incomplete algorithms is that they
scale better than their complete counterparts. However, to make an incomplete
algorithm effective one needs to guarantee that the probability of finding a
bug is reasonably high. We try to achieve such effectiveness by employing the
Test-As-Proofs (TAP) paradigm. In our TAP based approach, a counterexample is
built as a sequence of states extracted from proofs that some local variations
of property P hold. This increases the probability that a) a representative set
of states is examined and that b) the considered states are relevant to
property P.
We describe an algorithm of test generation based on the TAP paradigm and
give preliminary experimental results
Scalable Parallel Numerical Constraint Solver Using Global Load Balancing
We present a scalable parallel solver for numerical constraint satisfaction
problems (NCSPs). Our parallelization scheme consists of homogeneous worker
solvers, each of which runs on an available core and communicates with others
via the global load balancing (GLB) method. The parallel solver is implemented
with X10 that provides an implementation of GLB as a library. In experiments,
several NCSPs from the literature were solved and attained up to 516-fold
speedup using 600 cores of the TSUBAME2.5 supercomputer.Comment: To be presented at X10'15 Worksho
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