Online Permutation Routing in Partitioned Optical Passive Star Networks

This paper establishes the state of the art in both deterministic and randomized online permutation routing in the POPS network. Indeed, we show that any permutation can be routed online on a POPS network either with $O(\frac{d}{g}\log g)$ deterministic slots, or, with high probability, with $5c\lceil d/g\rceil+o(d/g)+O(\log\log g)$ randomized slots, where constant $c=\exp (1+e^{-1})\approx 3.927$. When $d=\Theta(g)$, that we claim to be the "interesting" case, the randomized algorithm is exponentially faster than any other algorithm in the literature, both deterministic and randomized ones. This is true in practice as well. Indeed, experiments show that it outperforms its rivals even starting from as small a network as a POPS(2,2), and the gap grows exponentially with the size of the network. We can also show that, under proper hypothesis, no deterministic algorithm can asymptotically match its performance

Optimal parallel string algorithms: sorting, merching and computing the minimum

We study fundamental comparison problems on strings of characters, equipped with the usual lexicographical ordering. For each problem studied, we give a parallel algorithm that is optimal with respect to at least one criterion for which no optimal algorithm was previously known. Specifically, our main results are: % \begin{itemize} \item Two sorted sequences of strings, containing altogether $n$~characters, can be merged in $O(\log n)$ time using $O(n)$ operations on an EREW PRAM. This is optimal as regards both the running time and the number of operations. \item A sequence of strings, containing altogether $n$~characters represented by integers of size polynomial in~$n$, can be sorted in $O({{\log n}/{\log\log n}})$ time using $O(n\log\log n)$ operations on a CRCW PRAM. The running time is optimal for any polynomial number of processors. \item The minimum string in a sequence of strings containing altogether $n$ characters can be found using (expected) $O(n)$ operations in constant expected time on a randomized CRCW PRAM, in $O(\log\log n)$ time on a deterministic CRCW PRAM with a program depending on~$n$, in $O((\log\log n)^3)$ time on a deterministic CRCW PRAM with a program not depending on~$n$, in $O(\log n)$ expected time on a randomized EREW PRAM, and in $O(\log n\log\log n)$ time on a deterministic EREW PRAM. The number of operations is optimal, and the running time is optimal for the randomized algorithms and, if the number of processors is limited to~$n$, for the nonuniform deterministic CRCW PRAM algorithm as we

Hardware Based Projection onto The Parity Polytope and Probability Simplex

This paper is concerned with the adaptation to hardware of methods for Euclidean norm projections onto the parity polytope and probability simplex. We first refine recent efforts to develop efficient methods of projection onto the parity polytope. Our resulting algorithm can be configured to have either average computational complexity $\mathcal{O}\left(d\right)$ or worst case complexity $\mathcal{O}\left(d\log{d}\right)$ on a serial processor where $d$ is the dimension of projection space. We show how to adapt our projection routine to hardware. Our projection method uses a sub-routine that involves another Euclidean projection; onto the probability simplex. We therefore explain how to adapt to hardware a well know simplex projection algorithm. The hardware implementations of both projection algorithms achieve area scalings of $\mathcal{O}(d\left(\log{d}\right)^2)$ at a delay of $\mathcal{O}(\left(\log{d}\right)^2)$. Finally, we present numerical results in which we evaluate the fixed-point accuracy and resource scaling of these algorithms when targeting a modern FPGA

Meaning in Life for Patients With Severe Dementia: A Qualitative Study of Healthcare Professionals' Interpretations

The need for meaning in life is a key aspect of being human, and a central issue in the psychology of religion. Understanding experience of meaning for persons with severe dementia is challenging due to the impairments associated with the illness. Despite these challenges, this article argues that meaning in life is as important for a person with severe dementia as it is for everyone else. This study was conducted in a Norwegian hospital and nursing home context and was part of a research project on meaning in life for persons with severe dementia. The study builds on two other studies which focused on how meaning-making and experience of meaningfulness appeared in patients with severe dementia. By presenting the findings from these two studies for a group of healthcare professionals and introducing them to research on meaning in life, the aim of this study was to explore how healthcare professionals interpret the patients' experience of meaning in life in practise for patients with severe dementia in a hospital and nursing home context, and to highlight its clinical implications. The study was conducted using a qualitative method with exploratory design. The data were collected at a round table conference, a method inspired by a mode of action research called “co-operative inquiry.” Altogether 27 professional healthcarers, from a variety of professions, with high competence in dementia care participated together with six researchers authoring this article. This study revealed that healthcare professionals were constantly dealing with different forms of meaning in their everyday care for people with dementia. The findings also showed clear connexions between understanding of meaning and fundamental aspects of good dementia care. Meaning corresponded well with the principles of person-centred care, and this compatibility allowed the healthcare professionals to associate meaning in life as a perspective into their work without having much prior knowledge or being familiar with the use of this perspective. The study points out that awareness of meaning in life as an integrated perspective in clinical practise will contribute to a broader and enhanced repertoire, and hence to improved dementia care. Facilitating experience of meaning calls for increased resources in personnel and competence in future dementia care.publishedVersio

The VLSI Optimality of the AKS Sorting Network

Coordinated Science Laboratory was formerly known as Control Systems LaboratoryJoint Services Electronics Program / N00014-79-C-0424IBM Predoctoral Fellowship Progra

Secure Merge with O(n log log n) Secure Operations

Data-oblivious algorithms are a key component of many secure computation protocols. In this work, we show that advances in secure multiparty shuffling algorithms can be used to increase the efficiency of several key cryptographic tools. The key observation is that many secure computation protocols rely heavily on secure shuffles. The best data-oblivious shuffling algorithms require $O(n \log n)$, operations, but in the two-party or multiparty setting, secure shuffling can be achieved with only $O(n)$ communication. Leveraging the efficiency of secure multiparty shuffling, we give novel algorithms that improve the efficiency of securely sorting sparse lists, secure stable compaction, and securely merging two sorted lists. Securely sorting private lists is a key component of many larger secure computation protocols. The best data-oblivious sorting algorithms for sorting a list of $n$ elements require $O(n \log n)$ comparisons. Using black-box access to a linear-communication secure shuffle, we give a secure algorithm for sorting a list of length $n$ with $t \ll n$ nonzero elements with communication $O(t \log^2 n + n)$, which beats the best oblivious algorithms when the number of nonzero elements, $t$, satisfies $t < n/\log^2 n$. Secure compaction is the problem of removing dummy elements from a list, and is essentially equivalent to sorting on 1-bit keys. The best oblivious compaction algorithms run in $O(n)$-time, but they are unstable, i.e., the order of the remaining elements is not preserved. Using black-box access to a linear-communication secure shuffle, we give a stable compaction algorithm with only $O(n)$ communication. Our main result is a novel secure merge protocol. The best previous algorithms for securely merging two sorted lists into a sorted whole required $O(n \log n)$ secure operations. Using black-box access to an $O(n)$-communication secure shuffle, we give the first secure merge algorithm that requires only $O(n \log \log n)$ communication. Our algorithm takes as input $n$ secret-shared values, and outputs a secret-sharing of the sorted list. All our algorithms are generic, i.e., they can be implemented using generic secure computations techniques and make black-box access to a secure shuffle. Our techniques extend naturally to the multiparty situation (with a constant number of parties) as well as to handle malicious adversaries without changing the asymptotic efficiency. These algorithm have applications to securely computing database joins and order statistics on private data as well as multiparty Oblivious RAM protocols