3,632 research outputs found
The Capacity of Smartphone Peer-To-Peer Networks
We study three capacity problems in the mobile telephone model, a network abstraction that models the peer-to-peer communication capabilities implemented in most commodity smartphone operating systems. The capacity of a network expresses how much sustained throughput can be maintained for a set of communication demands, and is therefore a fundamental bound on the usefulness of a network. Because of this importance, wireless network capacity has been active area of research for the last two decades.
The three capacity problems that we study differ in the structure of the communication demands. The first problem is pairwise capacity, where the demands are (source, destination) pairs. Pairwise capacity is one of the most classical definitions, as it was analyzed in the seminal paper of Gupta and Kumar on wireless network capacity. The second problem we study is broadcast capacity, in which a single source must deliver packets to all other nodes in the network. Finally, we turn our attention to all-to-all capacity, in which all nodes must deliver packets to all other nodes. In all three of these problems we characterize the optimal achievable throughput for any given network, and design algorithms which asymptotically match this performance. We also study these problems in networks generated randomly by a process introduced by Gupta and Kumar, and fully characterize their achievable throughput.
Interestingly, the techniques that we develop for all-to-all capacity also allow us to design a one-shot gossip algorithm that runs within a polylogarithmic factor of optimal in every graph. This largely resolves an open question from previous work on the one-shot gossip problem in this model
Approximate Deadline-Scheduling with Precedence Constraints
We consider the classic problem of scheduling a set of n jobs
non-preemptively on a single machine. Each job j has non-negative processing
time, weight, and deadline, and a feasible schedule needs to be consistent with
chain-like precedence constraints. The goal is to compute a feasible schedule
that minimizes the sum of penalties of late jobs. Lenstra and Rinnoy Kan
[Annals of Disc. Math., 1977] in their seminal work introduced this problem and
showed that it is strongly NP-hard, even when all processing times and weights
are 1. We study the approximability of the problem and our main result is an
O(log k)-approximation algorithm for instances with k distinct job deadlines
Scheduling trainees at a hospital department using a branch-and-price approach.
Scheduling trainees (graduate students) is a complicated problem that has to be solved frequently in many hospital departments. We will describe a trainee scheduling problem encountered in practice (at the ophthalmology department of the university hospital Gasthuisberg, Leuven). In this problem a department has a certain number of trainees at its disposal, which assist specialists in their activities (surgery, consultation, etc.). For each trainee one has to schedule the activities in which (s)he will assist during a certain time horizon, usually one year. Typically, these kind of scheduling problems are characterized by both hard and soft constraints. The hard constraints consist of both work covering constraints and formation requirements, whereas the soft constraints include trainees' preferences and setup restrictions. In this paper we will describe an exact branch-and-price method to solve the problem to optimality.Branch-and-price; Constraint; Health care; Problems; Requirements; Scheduling; Staff scheduling; Time; University;
Hierarchical fractional-step approximations and parallel kinetic Monte Carlo algorithms
We present a mathematical framework for constructing and analyzing parallel
algorithms for lattice Kinetic Monte Carlo (KMC) simulations. The resulting
algorithms have the capacity to simulate a wide range of spatio-temporal scales
in spatially distributed, non-equilibrium physiochemical processes with complex
chemistry and transport micro-mechanisms. The algorithms can be tailored to
specific hierarchical parallel architectures such as multi-core processors or
clusters of Graphical Processing Units (GPUs). The proposed parallel algorithms
are controlled-error approximations of kinetic Monte Carlo algorithms,
departing from the predominant paradigm of creating parallel KMC algorithms
with exactly the same master equation as the serial one.
Our methodology relies on a spatial decomposition of the Markov operator
underlying the KMC algorithm into a hierarchy of operators corresponding to the
processors' structure in the parallel architecture. Based on this operator
decomposition, we formulate Fractional Step Approximation schemes by employing
the Trotter Theorem and its random variants; these schemes, (a) determine the
communication schedule} between processors, and (b) are run independently on
each processor through a serial KMC simulation, called a kernel, on each
fractional step time-window.
Furthermore, the proposed mathematical framework allows us to rigorously
justify the numerical and statistical consistency of the proposed algorithms,
showing the convergence of our approximating schemes to the original serial
KMC. The approach also provides a systematic evaluation of different processor
communicating schedules.Comment: 34 pages, 9 figure
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