3 research outputs found
Optimal phase estimation in quantum networks
We address the problem of estimating the phase phi given N copies of the
phase rotation u(phi) within an array of quantum operations in finite
dimensions. We first consider the special case where the array consists of an
arbitrary input state followed by any arrangement of the N phase rotations, and
ending with a POVM. We optimise the POVM for a given input state and fixed
arrangement. Then we also optimise the input state for some specific cost
functions. In all cases, the optimal POVM is equivalent to a quantum Fourier
transform in an appropriate basis. Examples and applications are given.Comment: 9 pages, 2 figures; this is an extended version of
arXiv:quant-ph/0609160. v2: minor corrections in reference
On Multi-dimensional Packing Problems
We study the approximability of multi-dimensional generalizations of three classical packing problems: multiprocessor scheduling, bin packing, and the knapsack problem. Specifically, we study the vector scheduling problem, its dual problem, namely, the vector bin packing problem, and a class of packing integer programs. The vector scheduling problem is to schedule n d-dimensional tasks on m machines such that the maximum load over all dimensions and all machines is minimized. The vector bin packing problem, on the other hand, seeks to minimize the number of bins needed to schedule all n tasks such that the maximum load on any dimension accross all bins is bounded by a fixed quantity, say 1. Such problems naturally arise when scheduling tasks that have multiple resource requirements. Finally, packing integer programs capture a core problem that directly relates to both vector scheduling and vector bin packing, namely, the problem of packing a miximum number of vectors in a single bin of unit height. We obtain a variety of new algorithmic as well as inapproximability results for these three problems
Data-driven exploration of mobility interaction patterns
In this thesis we propose an analysis framework for studying the interactions between moving objects, such as cars on roads, pedestrians in a square, etc. We follow a data mining approach, based on the computation of simple interaction events and on the extraction of complex patterns, describing frequent combinations of events that happen together and their evolution in time. The work includes two case studies on real datasets, respectively on cars and roads