45,382 research outputs found
Input-Dynamic Distributed Algorithms for Communication Networks
Consider a distributed task where the communication network is fixed but the
local inputs given to the nodes of the distributed system may change over time.
In this work, we explore the following question: if some of the local inputs
change, can an existing solution be updated efficiently, in a dynamic and
distributed manner?
To address this question, we define the batch dynamic CONGEST model in which
we are given a bandwidth-limited communication network and a dynamic edge
labelling defines the problem input. The task is to maintain a solution to a
graph problem on the labeled graph under batch changes. We investigate, when a
batch of edge label changes arrive,
-- how much time as a function of we need to update an existing
solution, and
-- how much information the nodes have to keep in local memory between
batches in order to update the solution quickly.
Our work lays the foundations for the theory of input-dynamic distributed
network algorithms. We give a general picture of the complexity landscape in
this model, design both universal algorithms and algorithms for concrete
problems, and present a general framework for lower bounds. In particular, we
derive non-trivial upper bounds for two selected, contrasting problems:
maintaining a minimum spanning tree and detecting cliques
Optimal Algorithms for Ranked Enumeration of Answers to Full Conjunctive Queries
We study ranked enumeration of join-query results according to very general
orders defined by selective dioids. Our main contribution is a framework for
ranked enumeration over a class of dynamic programming problems that
generalizes seemingly different problems that had been studied in isolation. To
this end, we extend classic algorithms that find the k-shortest paths in a
weighted graph. For full conjunctive queries, including cyclic ones, our
approach is optimal in terms of the time to return the top result and the delay
between results. These optimality properties are derived for the widely used
notion of data complexity, which treats query size as a constant. By performing
a careful cost analysis, we are able to uncover a previously unknown tradeoff
between two incomparable enumeration approaches: one has lower complexity when
the number of returned results is small, the other when the number is very
large. We theoretically and empirically demonstrate the superiority of our
techniques over batch algorithms, which produce the full result and then sort
it. Our technique is not only faster for returning the first few results, but
on some inputs beats the batch algorithm even when all results are produced.Comment: 50 pages, 19 figure
Batch Informed Trees (BIT*): Sampling-based Optimal Planning via the Heuristically Guided Search of Implicit Random Geometric Graphs
In this paper, we present Batch Informed Trees (BIT*), a planning algorithm
based on unifying graph- and sampling-based planning techniques. By recognizing
that a set of samples describes an implicit random geometric graph (RGG), we
are able to combine the efficient ordered nature of graph-based techniques,
such as A*, with the anytime scalability of sampling-based algorithms, such as
Rapidly-exploring Random Trees (RRT).
BIT* uses a heuristic to efficiently search a series of increasingly dense
implicit RGGs while reusing previous information. It can be viewed as an
extension of incremental graph-search techniques, such as Lifelong Planning A*
(LPA*), to continuous problem domains as well as a generalization of existing
sampling-based optimal planners. It is shown that it is probabilistically
complete and asymptotically optimal.
We demonstrate the utility of BIT* on simulated random worlds in
and and manipulation problems on CMU's HERB, a
14-DOF two-armed robot. On these problems, BIT* finds better solutions faster
than RRT, RRT*, Informed RRT*, and Fast Marching Trees (FMT*) with faster
anytime convergence towards the optimum, especially in high dimensions.Comment: 8 Pages. 6 Figures. Video available at
http://www.youtube.com/watch?v=TQIoCC48gp
Batch Informed Trees (BIT*): Informed Asymptotically Optimal Anytime Search
Path planning in robotics often requires finding high-quality solutions to
continuously valued and/or high-dimensional problems. These problems are
challenging and most planning algorithms instead solve simplified
approximations. Popular approximations include graphs and random samples, as
respectively used by informed graph-based searches and anytime sampling-based
planners. Informed graph-based searches, such as A*, traditionally use
heuristics to search a priori graphs in order of potential solution quality.
This makes their search efficient but leaves their performance dependent on the
chosen approximation. If its resolution is too low then they may not find a
(suitable) solution but if it is too high then they may take a prohibitively
long time to do so. Anytime sampling-based planners, such as RRT*,
traditionally use random sampling to approximate the problem domain
incrementally. This allows them to increase resolution until a suitable
solution is found but makes their search dependent on the order of
approximation. Arbitrary sequences of random samples approximate the problem
domain in every direction simultaneously and but may be prohibitively
inefficient at containing a solution. This paper unifies and extends these two
approaches to develop Batch Informed Trees (BIT*), an informed, anytime
sampling-based planner. BIT* solves continuous path planning problems
efficiently by using sampling and heuristics to alternately approximate and
search the problem domain. Its search is ordered by potential solution quality,
as in A*, and its approximation improves indefinitely with additional
computational time, as in RRT*. It is shown analytically to be almost-surely
asymptotically optimal and experimentally to outperform existing sampling-based
planners, especially on high-dimensional planning problems.Comment: International Journal of Robotics Research (IJRR). 32 Pages. 16
Figure
Fully-dynamic Approximation of Betweenness Centrality
Betweenness is a well-known centrality measure that ranks the nodes of a
network according to their participation in shortest paths. Since an exact
computation is prohibitive in large networks, several approximation algorithms
have been proposed. Besides that, recent years have seen the publication of
dynamic algorithms for efficient recomputation of betweenness in evolving
networks. In previous work we proposed the first semi-dynamic algorithms that
recompute an approximation of betweenness in connected graphs after batches of
edge insertions.
In this paper we propose the first fully-dynamic approximation algorithms
(for weighted and unweighted undirected graphs that need not to be connected)
with a provable guarantee on the maximum approximation error. The transfer to
fully-dynamic and disconnected graphs implies additional algorithmic problems
that could be of independent interest. In particular, we propose a new upper
bound on the vertex diameter for weighted undirected graphs. For both weighted
and unweighted graphs, we also propose the first fully-dynamic algorithms that
keep track of such upper bound. In addition, we extend our former algorithm for
semi-dynamic BFS to batches of both edge insertions and deletions.
Using approximation, our algorithms are the first to make in-memory
computation of betweenness in fully-dynamic networks with millions of edges
feasible. Our experiments show that they can achieve substantial speedups
compared to recomputation, up to several orders of magnitude
Fully dynamic all-pairs shortest paths with worst-case update-time revisited
We revisit the classic problem of dynamically maintaining shortest paths
between all pairs of nodes of a directed weighted graph. The allowed updates
are insertions and deletions of nodes and their incident edges. We give
worst-case guarantees on the time needed to process a single update (in
contrast to related results, the update time is not amortized over a sequence
of updates).
Our main result is a simple randomized algorithm that for any parameter
has a worst-case update time of and answers
distance queries correctly with probability , against an adaptive
online adversary if the graph contains no negative cycle. The best
deterministic algorithm is by Thorup [STOC 2005] with a worst-case update time
of and assumes non-negative weights. This is the first
improvement for this problem for more than a decade. Conceptually, our
algorithm shows that randomization along with a more direct approach can
provide better bounds.Comment: To be presented at the Symposium on Discrete Algorithms (SODA) 201
- …