641 research outputs found
Deterministic Computations on a PRAM with Static Processor and Memory Faults.
We consider Parallel Random Access Machine (PRAM) which has some processors
and memory cells faulty. The faults considered are static, i.e., once the
machine starts to operate, the operational/faulty status of PRAM components
does not change. We develop a deterministic simulation of a fully operational
PRAM on a similar faulty machine which has constant fractions of faults among
processors and memory cells. The simulating PRAM has processors and
memory cells, and simulates a PRAM with processors and a constant fraction
of memory cells. The simulation is in two phases: it starts with
preprocessing, which is followed by the simulation proper performed in a
step-by-step fashion. Preprocessing is performed in time . The slowdown of a step-by-step part of the simulation is
Minimizing Flow Time in the Wireless Gathering Problem
We address the problem of efficient data gathering in a wireless network
through multi-hop communication. We focus on the objective of minimizing the
maximum flow time of a data packet. We prove that no polynomial time algorithm
for this problem can have approximation ratio less than \Omega(m^{1/3) when
packets have to be transmitted, unless . We then use resource
augmentation to assess the performance of a FIFO-like strategy. We prove that
this strategy is 5-speed optimal, i.e., its cost remains within the optimal
cost if we allow the algorithm to transmit data at a speed 5 times higher than
that of the optimal solution we compare to
Almost Universal Anonymous Rendezvous in the Plane
Two mobile agents represented by points freely moving in the plane and
starting at two distinct positions, have to meet. The meeting, called
rendezvous, occurs when agents are at distance at most of each other and
never move after this time, where is a positive real unknown to them,
called the visibility radius. Agents are anonymous and execute the same
deterministic algorithm. Each agent has a set of private attributes, some or
all of which can differ between agents. These attributes are: the initial
position of the agent, its system of coordinates (orientation and chirality),
the rate of its clock, its speed when it moves, and the time of its wake-up. If
all attributes (except the initial positions) are identical and agents start at
distance larger than then they can never meet. However, differences between
attributes make it sometimes possible to break the symmetry and accomplish
rendezvous. Such instances of the rendezvous problem (formalized as lists of
attributes), are called feasible.
Our contribution is three-fold. We first give an exact characterization of
feasible instances. Thus it is natural to ask whether there exists a single
algorithm that guarantees rendezvous for all these instances. We give a strong
negative answer to this question: we show two sets and of feasible
instances such that none of them admits a single rendezvous algorithm valid for
all instances of the set. On the other hand, we construct a single algorithm
that guarantees rendezvous for all feasible instances outside of sets and
. We observe that these exception sets and are geometrically
very small, compared to the set of all feasible instances: they are included in
low-dimension subspaces of the latter. Thus, our rendezvous algorithm handling
all feasible instances other than these small sets of exceptions can be justly
called almost universal
Upconversion of optical signals with multi-longitudinal-mode pump lasers
Multi-longitudinal-mode lasers have been believed to be good candidates as
pump sources for optical frequency conversion. However, we present a
semi-classical model for frequency conversion of optical signals with a
multimode pump laser, which shows that fluctuations of the instantaneous pump
power limit the conversion efficiency. In an experiment, we upconverted a 1550
nm optical signal in a periodically poled lithium niobate waveguide using with
a multi-longitudinal-mode laser, an observed a maximum conversion efficiency of
70%, in good agreement with our theoretical model. Compared to single-mode
pumping, multimode pumping is not a suitable technique for attaining stable
near-unity-efficiency frequency conversion. However, the results obtained here
could find application in characterization of the spectral or temporal
structure of multi-longitudinal-mode lasers.Comment: 6 pages, 4 figures, comments are welcome
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