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 $n$ processors and $m$ memory cells, and simulates a PRAM with $n$ processors and a constant fraction of $m$ 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 $O((\frac{m}{n}+ \log n)\log n)$. The slowdown of a step-by-step part of the simulation is $O(\log m)$

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 $m$ packets have to be transmitted, unless $P = NP$. 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 $r$ of each other and never move after this time, where $r$ 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 $r$ 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 $S_1$ and $S_2$ 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 $S_1$ and $S_2$. We observe that these exception sets $S_1$ and $S_2$ 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