274 research outputs found
Parallel Batch-Dynamic Graph Connectivity
In this paper, we study batch parallel algorithms for the dynamic
connectivity problem, a fundamental problem that has received considerable
attention in the sequential setting. The most well known sequential algorithm
for dynamic connectivity is the elegant level-set algorithm of Holm, de
Lichtenberg and Thorup (HDT), which achieves amortized time per
edge insertion or deletion, and time per query. We
design a parallel batch-dynamic connectivity algorithm that is work-efficient
with respect to the HDT algorithm for small batch sizes, and is asymptotically
faster when the average batch size is sufficiently large. Given a sequence of
batched updates, where is the average batch size of all deletions, our
algorithm achieves expected amortized work per
edge insertion and deletion and depth w.h.p. Our algorithm
answers a batch of connectivity queries in expected
work and depth w.h.p. To the best of our knowledge, our algorithm
is the first parallel batch-dynamic algorithm for connectivity.Comment: This is the full version of the paper appearing in the ACM Symposium
on Parallelism in Algorithms and Architectures (SPAA), 201
Adaptive Regret Minimization in Bounded-Memory Games
Online learning algorithms that minimize regret provide strong guarantees in
situations that involve repeatedly making decisions in an uncertain
environment, e.g. a driver deciding what route to drive to work every day.
While regret minimization has been extensively studied in repeated games, we
study regret minimization for a richer class of games called bounded memory
games. In each round of a two-player bounded memory-m game, both players
simultaneously play an action, observe an outcome and receive a reward. The
reward may depend on the last m outcomes as well as the actions of the players
in the current round. The standard notion of regret for repeated games is no
longer suitable because actions and rewards can depend on the history of play.
To account for this generality, we introduce the notion of k-adaptive regret,
which compares the reward obtained by playing actions prescribed by the
algorithm against a hypothetical k-adaptive adversary with the reward obtained
by the best expert in hindsight against the same adversary. Roughly, a
hypothetical k-adaptive adversary adapts her strategy to the defender's actions
exactly as the real adversary would within each window of k rounds. Our
definition is parametrized by a set of experts, which can include both fixed
and adaptive defender strategies.
We investigate the inherent complexity of and design algorithms for adaptive
regret minimization in bounded memory games of perfect and imperfect
information. We prove a hardness result showing that, with imperfect
information, any k-adaptive regret minimizing algorithm (with fixed strategies
as experts) must be inefficient unless NP=RP even when playing against an
oblivious adversary. In contrast, for bounded memory games of perfect and
imperfect information we present approximate 0-adaptive regret minimization
algorithms against an oblivious adversary running in time n^{O(1)}.Comment: Full Version. GameSec 2013 (Invited Paper
Collaborative Delivery with Energy-Constrained Mobile Robots
We consider the problem of collectively delivering some message from a
specified source to a designated target location in a graph, using multiple
mobile agents. Each agent has a limited energy which constrains the distance it
can move. Hence multiple agents need to collaborate to move the message, each
agent handing over the message to the next agent to carry it forward. Given the
positions of the agents in the graph and their respective budgets, the problem
of finding a feasible movement schedule for the agents can be challenging. We
consider two variants of the problem: in non-returning delivery, the agents can
stop anywhere; whereas in returning delivery, each agent needs to return to its
starting location, a variant which has not been studied before.
We first provide a polynomial-time algorithm for returning delivery on trees,
which is in contrast to the known (weak) NP-hardness of the non-returning
version. In addition, we give resource-augmented algorithms for returning
delivery in general graphs. Finally, we give tight lower bounds on the required
resource augmentation for both variants of the problem. In this sense, our
results close the gap left by previous research.Comment: 19 pages. An extended abstract of this paper was published at the
23rd International Colloquium on Structural Information and Communication
Complexity 2016, SIROCCO'1
Acoustic emission during fatigue of Ti-6Al-4V: Incipient fatigue crack detection limits and generalized data analysis methodology
The fundamentals associated with acoustic emission monitoring of fatigue crack initiation and propagation of Ti-6Al-4V were studied. Acoustic emission can detect and locate incipient fatigue crack extensions of approximately 10 μm. The technique therefore can serve as a sensitive warning to material failure. There are three distinct stages during which acoustic emission is generated. These stages are: crack initiation, slow crack propagation and rapid crack propagation. The distinction between the stages is based primarily on the rate of acoustic emission event accumulation. These three stages of acoustic emission correspond to the three stages of the failure process that occurs during fatigue loading. That is, changes in acoustic emission event rate correspond to changes in crack extension rate. Acoustic emission event intensities are greater during crack initiation than during slow crack propagation and greatest during rapid crack propagation. In a given fatigue cycle, event intensities increase with increasing stress and most high-intensity events occur near or at the maximum stress. Acoustic emission may therefore be used with confidence to detect, monitor and anticipate failure, in real-time.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/44713/1/10853_2005_Article_BF01116003.pd
A general lower bound for collaborative tree exploration
We consider collaborative graph exploration with a set of agents. All
agents start at a common vertex of an initially unknown graph and need to
collectively visit all other vertices. We assume agents are deterministic,
vertices are distinguishable, moves are simultaneous, and we allow agents to
communicate globally. For this setting, we give the first non-trivial lower
bounds that bridge the gap between small () and large () teams of agents. Remarkably, our bounds tightly connect to existing results
in both domains.
First, we significantly extend a lower bound of
by Dynia et al. on the competitive ratio of a collaborative tree exploration
strategy to the range for any . Second,
we provide a tight lower bound on the number of agents needed for any
competitive exploration algorithm. In particular, we show that any
collaborative tree exploration algorithm with agents has a
competitive ratio of , while Dereniowski et al. gave an algorithm
with agents and competitive ratio , for any
and with denoting the diameter of the graph. Lastly, we
show that, for any exploration algorithm using agents, there exist
trees of arbitrarily large height that require rounds, and we
provide a simple algorithm that matches this bound for all trees
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