2,292 research outputs found
Symmetry-Based Search Space Reduction For Grid Maps
In this paper we explore a symmetry-based search space reduction technique
which can speed up optimal pathfinding on undirected uniform-cost grid maps by
up to 38 times. Our technique decomposes grid maps into a set of empty
rectangles, removing from each rectangle all interior nodes and possibly some
from along the perimeter. We then add a series of macro-edges between selected
pairs of remaining perimeter nodes to facilitate provably optimal traversal
through each rectangle. We also develop a novel online pruning technique to
further speed up search. Our algorithm is fast, memory efficient and retains
the same optimality and completeness guarantees as searching on an unmodified
grid map
Taming Numbers and Durations in the Model Checking Integrated Planning System
The Model Checking Integrated Planning System (MIPS) is a temporal least
commitment heuristic search planner based on a flexible object-oriented
workbench architecture. Its design clearly separates explicit and symbolic
directed exploration algorithms from the set of on-line and off-line computed
estimates and associated data structures. MIPS has shown distinguished
performance in the last two international planning competitions. In the last
event the description language was extended from pure propositional planning to
include numerical state variables, action durations, and plan quality objective
functions. Plans were no longer sequences of actions but time-stamped
schedules. As a participant of the fully automated track of the competition,
MIPS has proven to be a general system; in each track and every benchmark
domain it efficiently computed plans of remarkable quality. This article
introduces and analyzes the most important algorithmic novelties that were
necessary to tackle the new layers of expressiveness in the benchmark problems
and to achieve a high level of performance. The extensions include critical
path analysis of sequentially generated plans to generate corresponding optimal
parallel plans. The linear time algorithm to compute the parallel plan bypasses
known NP hardness results for partial ordering by scheduling plans with respect
to the set of actions and the imposed precedence relations. The efficiency of
this algorithm also allows us to improve the exploration guidance: for each
encountered planning state the corresponding approximate sequential plan is
scheduled. One major strength of MIPS is its static analysis phase that grounds
and simplifies parameterized predicates, functions and operators, that infers
knowledge to minimize the state description length, and that detects domain
object symmetries. The latter aspect is analyzed in detail. MIPS has been
developed to serve as a complete and optimal state space planner, with
admissible estimates, exploration engines and branching cuts. In the
competition version, however, certain performance compromises had to be made,
including floating point arithmetic, weighted heuristic search exploration
according to an inadmissible estimate and parameterized optimization
Weak looking-ahead and its application in computer-integrated process planning
Constraint logic programming has been shown to be a very useful tool for knowledge representation and problem-solving in different areas. Finite Domain extensions of PROLOG together with efficient consistency techniques such as forward-checking and looking-ahead make it possible to solve many discrete combinatorial problems within a short development time. In this paper we present the weak looking-ahead strategy (WLA), a new consistency technique on finite domains combining the computational efficiency of forward-checking with the pruning power of looking-ahead. Moreover, incorporating weak looking-ahead into PROLOG\u27s SLD resolution gives a sound and complete inference rule whereas standard looking-ahead itself has been shown to be incomplete. Finally, we will show how to use weak looking-ahead in a real-world application to obtain an early search-space pruning while avoiding the control overhead involved by standard looking-ahead
Approximation algorithms for node-weighted prize-collecting Steiner tree problems on planar graphs
We study the prize-collecting version of the Node-weighted Steiner Tree
problem (NWPCST) restricted to planar graphs. We give a new primal-dual
Lagrangian-multiplier-preserving (LMP) 3-approximation algorithm for planar
NWPCST. We then show a ()-approximation which establishes a
new best approximation guarantee for planar NWPCST. This is done by combining
our LMP algorithm with a threshold rounding technique and utilizing the
2.4-approximation of Berman and Yaroslavtsev for the version without penalties.
We also give a primal-dual 4-approximation algorithm for the more general
forest version using techniques introduced by Hajiaghay and Jain
The GRT Planning System: Backward Heuristic Construction in Forward State-Space Planning
This paper presents GRT, a domain-independent heuristic planning system for
STRIPS worlds. GRT solves problems in two phases. In the pre-processing phase,
it estimates the distance between each fact and the goals of the problem, in a
backward direction. Then, in the search phase, these estimates are used in
order to further estimate the distance between each intermediate state and the
goals, guiding so the search process in a forward direction and on a best-first
basis. The paper presents the benefits from the adoption of opposite directions
between the preprocessing and the search phases, discusses some difficulties
that arise in the pre-processing phase and introduces techniques to cope with
them. Moreover, it presents several methods of improving the efficiency of the
heuristic, by enriching the representation and by reducing the size of the
problem. Finally, a method of overcoming local optimal states, based on domain
axioms, is proposed. According to it, difficult problems are decomposed into
easier sub-problems that have to be solved sequentially. The performance
results from various domains, including those of the recent planning
competitions, show that GRT is among the fastest planners
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