6,719 research outputs found
A Linearithmic Time Algorithm for a Shortest Vector Problem in Compute-and-Forward Design
We propose an algorithm with expected complexity of \bigO(n\log n)
arithmetic operations to solve a special shortest vector problem arising in
computer-and-forward design, where is the dimension of the channel vector.
This algorithm is more efficient than the best known algorithms with proved
complexity.Comment: It has been submitted to ISIT 201
Bayesian Active Edge Evaluation on Expensive Graphs
Robots operate in environments with varying implicit structure. For instance,
a helicopter flying over terrain encounters a very different arrangement of
obstacles than a robotic arm manipulating objects on a cluttered table top.
State-of-the-art motion planning systems do not exploit this structure, thereby
expending valuable planning effort searching for implausible solutions. We are
interested in planning algorithms that actively infer the underlying structure
of the valid configuration space during planning in order to find solutions
with minimal effort. Consider the problem of evaluating edges on a graph to
quickly discover collision-free paths. Evaluating edges is expensive, both for
robots with complex geometries like robot arms, and for robots with limited
onboard computation like UAVs. Until now, this challenge has been addressed via
laziness i.e. deferring edge evaluation until absolutely necessary, with the
hope that edges turn out to be valid. However, all edges are not alike in value
- some have a lot of potentially good paths flowing through them, and some
others encode the likelihood of neighbouring edges being valid. This leads to
our key insight - instead of passive laziness, we can actively choose edges
that reduce the uncertainty about the validity of paths. We show that this is
equivalent to the Bayesian active learning paradigm of decision region
determination (DRD). However, the DRD problem is not only combinatorially hard,
but also requires explicit enumeration of all possible worlds. We propose a
novel framework that combines two DRD algorithms, DIRECT and BISECT, to
overcome both issues. We show that our approach outperforms several
state-of-the-art algorithms on a spectrum of planning problems for mobile
robots, manipulators and autonomous helicopters
Lex-Partitioning: A New Option for BDD Search
For the exploration of large state spaces, symbolic search using binary
decision diagrams (BDDs) can save huge amounts of memory and computation time.
State sets are represented and modified by accessing and manipulating their
characteristic functions. BDD partitioning is used to compute the image as the
disjunction of smaller subimages.
In this paper, we propose a novel BDD partitioning option. The partitioning
is lexicographical in the binary representation of the states contained in the
set that is represented by a BDD and uniform with respect to the number of
states represented. The motivation of controlling the state set sizes in the
partitioning is to eventually bridge the gap between explicit and symbolic
search.
Let n be the size of the binary state vector. We propose an O(n) ranking and
unranking scheme that supports negated edges and operates on top of precomputed
satcount values. For the uniform split of a BDD, we then use unranking to
provide paths along which we partition the BDDs. In a shared BDD representation
the efforts are O(n). The algorithms are fully integrated in the CUDD library
and evaluated in strongly solving general game playing benchmarks.Comment: In Proceedings GRAPHITE 2012, arXiv:1210.611
Near-Optimal Approximate Shortest Paths and Transshipment in Distributed and Streaming Models
We present a method for solving the transshipment problem - also known as
uncapacitated minimum cost flow - up to a multiplicative error of in undirected graphs with non-negative edge weights using a
tailored gradient descent algorithm. Using to hide
polylogarithmic factors in (the number of nodes in the graph), our gradient
descent algorithm takes iterations, and in each
iteration it solves an instance of the transshipment problem up to a
multiplicative error of . In particular, this allows
us to perform a single iteration by computing a solution on a sparse spanner of
logarithmic stretch. Using a randomized rounding scheme, we can further extend
the method to finding approximate solutions for the single-source shortest
paths (SSSP) problem. As a consequence, we improve upon prior work by obtaining
the following results: (1) Broadcast CONGEST model: -approximate SSSP using rounds, where is the (hop) diameter of the network.
(2) Broadcast congested clique model: -approximate
transshipment and SSSP using rounds. (3)
Multipass streaming model: -approximate transshipment and
SSSP using space and passes. The
previously fastest SSSP algorithms for these models leverage sparse hop sets.
We bypass the hop set construction; computing a spanner is sufficient with our
method. The above bounds assume non-negative edge weights that are polynomially
bounded in ; for general non-negative weights, running times scale with the
logarithm of the maximum ratio between non-zero weights.Comment: Accepted to SIAM Journal on Computing. Preliminary version in DISC
2017. Abstract shortened to fit arXiv's limitation to 1920 character
- âŠ