374 research outputs found
The Unreasonable Success of Local Search: Geometric Optimization
What is the effectiveness of local search algorithms for geometric problems
in the plane? We prove that local search with neighborhoods of magnitude
is an approximation scheme for the following problems in the
Euclidian plane: TSP with random inputs, Steiner tree with random inputs,
facility location (with worst case inputs), and bicriteria -median (also
with worst case inputs). The randomness assumption is necessary for TSP
Dynamic Algorithms for the Massively Parallel Computation Model
The Massive Parallel Computing (MPC) model gained popularity during the last
decade and it is now seen as the standard model for processing large scale
data. One significant shortcoming of the model is that it assumes to work on
static datasets while, in practice, real-world datasets evolve continuously. To
overcome this issue, in this paper we initiate the study of dynamic algorithms
in the MPC model.
We first discuss the main requirements for a dynamic parallel model and we
show how to adapt the classic MPC model to capture them. Then we analyze the
connection between classic dynamic algorithms and dynamic algorithms in the MPC
model. Finally, we provide new efficient dynamic MPC algorithms for a variety
of fundamental graph problems, including connectivity, minimum spanning tree
and matching.Comment: Accepted to the 31st ACM Symposium on Parallelism in Algorithms and
Architectures (SPAA 2019
Two-dimensional topological quantum walks in the momentum space of structured light
Quantum walks are powerful tools for quantum applications and for designing
topological systems. Although they are simulated in a variety of platforms,
genuine two-dimensional realizations are still challenging. Here we present an
innovative approach to the photonic simulation of a quantum walk in two
dimensions, where walker positions are encoded in the transverse wavevector
components of a single light beam. The desired dynamics is obtained by means of
a sequence of liquid-crystal devices, which apply polarization-dependent
transverse "kicks" to the photons in the beam. We engineer our quantum walk so
that it realizes a periodically-driven Chern insulator, and we probe its
topological features by detecting the anomalous displacement of the photonic
wavepacket under the effect of a constant force. Our compact, versatile
platform offers exciting prospects for the photonic simulation of
two-dimensional quantum dynamics and topological systems.Comment: Published version of the manuscrip
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