11,535 research outputs found
Bidirectional Heuristic Search Reconsidered
The assessment of bidirectional heuristic search has been incorrect since it
was first published more than a quarter of a century ago. For quite a long
time, this search strategy did not achieve the expected results, and there was
a major misunderstanding about the reasons behind it. Although there is still
wide-spread belief that bidirectional heuristic search is afflicted by the
problem of search frontiers passing each other, we demonstrate that this
conjecture is wrong. Based on this finding, we present both a new generic
approach to bidirectional heuristic search and a new approach to dynamically
improving heuristic values that is feasible in bidirectional search only. These
approaches are put into perspective with both the traditional and more recently
proposed approaches in order to facilitate a better overall understanding.
Empirical results of experiments with our new approaches show that
bidirectional heuristic search can be performed very efficiently and also with
limited memory. These results suggest that bidirectional heuristic search
appears to be better for solving certain difficult problems than corresponding
unidirectional search. This provides some evidence for the usefulness of a
search strategy that was long neglected. In summary, we show that bidirectional
heuristic search is viable and consequently propose that it be reconsidered.Comment: See http://www.jair.org/ for any accompanying file
A Fast Algorithm Finding the Shortest Reset Words
In this paper we present a new fast algorithm finding minimal reset words for
finite synchronizing automata. The problem is know to be computationally hard,
and our algorithm is exponential. Yet, it is faster than the algorithms used so
far and it works well in practice. The main idea is to use a bidirectional BFS
and radix (Patricia) tries to store and compare resulted subsets. We give both
theoretical and practical arguments showing that the branching factor is
reduced efficiently. As a practical test we perform an experimental study of
the length of the shortest reset word for random automata with states and 2
input letters. We follow Skvorsov and Tipikin, who have performed such a study
using a SAT solver and considering automata up to states. With our
algorithm we are able to consider much larger sample of automata with up to
states. In particular, we obtain a new more precise estimation of the
expected length of the shortest reset word .Comment: COCOON 2013. The final publication is available at
http://link.springer.com/chapter/10.1007%2F978-3-642-38768-5_1
Determination of the Topology of a Directed Network
We consider strongly-connected directed networks of identical synchronous,
finite-state processors with in- and out-degree uniformly bounded by a network
constant. Via a straightforward extension of Ostrovsky and Wilkerson's
Backwards Communication Algorithm in [OW], we exhibit a protocol which solves
the Global Topology Determination Problem, the problem of having the root
processor map the global topology of a network of unknown size and topology,
with running time O(ND) where N represents the number of processors and D
represents the diameter of the network. A simple counting argument suffices to
show that the Global Topology Determination Problem has time-complexity Omega(N
logN) which makes the protocol presented asymptotically time-optimal for many
large networks.Comment: 9 pages, no figures, accepted to appear in IPDPS 2002 (unable to
attend), (journal version to appear in Information Processing Letters
Route Planning in Transportation Networks
We survey recent advances in algorithms for route planning in transportation
networks. For road networks, we show that one can compute driving directions in
milliseconds or less even at continental scale. A variety of techniques provide
different trade-offs between preprocessing effort, space requirements, and
query time. Some algorithms can answer queries in a fraction of a microsecond,
while others can deal efficiently with real-time traffic. Journey planning on
public transportation systems, although conceptually similar, is a
significantly harder problem due to its inherent time-dependent and
multicriteria nature. Although exact algorithms are fast enough for interactive
queries on metropolitan transit systems, dealing with continent-sized instances
requires simplifications or heavy preprocessing. The multimodal route planning
problem, which seeks journeys combining schedule-based transportation (buses,
trains) with unrestricted modes (walking, driving), is even harder, relying on
approximate solutions even for metropolitan inputs.Comment: This is an updated version of the technical report MSR-TR-2014-4,
previously published by Microsoft Research. This work was mostly done while
the authors Daniel Delling, Andrew Goldberg, and Renato F. Werneck were at
Microsoft Research Silicon Valle
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