Quicksort, Largest Bucket, and Min-Wise Hashing with Limited Independence

Randomized algorithms and data structures are often analyzed under the assumption of access to a perfect source of randomness. The most fundamental metric used to measure how "random" a hash function or a random number generator is, is its independence: a sequence of random variables is said to be $k$-independent if every variable is uniform and every size $k$ subset is independent. In this paper we consider three classic algorithms under limited independence. We provide new bounds for randomized quicksort, min-wise hashing and largest bucket size under limited independence. Our results can be summarized as follows. -Randomized quicksort. When pivot elements are computed using a $5$-independent hash function, Karloff and Raghavan, J.ACM'93 showed $O ( n \log n)$ expected worst-case running time for a special version of quicksort. We improve upon this, showing that the same running time is achieved with only $4$-independence. -Min-wise hashing. For a set $A$, consider the probability of a particular element being mapped to the smallest hash value. It is known that $5$-independence implies the optimal probability $O (1 /n)$. Broder et al., STOC'98 showed that $2$-independence implies it is $O(1 / \sqrt{|A|})$. We show a matching lower bound as well as new tight bounds for $3$- and $4$-independent hash functions. -Largest bucket. We consider the case where $n$ balls are distributed to $n$ buckets using a $k$-independent hash function and analyze the largest bucket size. Alon et. al, STOC'97 showed that there exists a $2$-independent hash function implying a bucket of size $\Omega ( n^{1/2})$. We generalize the bound, providing a $k$-independent family of functions that imply size $\Omega ( n^{1/k})$.Comment: Submitted to ICALP 201

Matchings on infinite graphs

Elek and Lippner (2010) showed that the convergence of a sequence of bounded-degree graphs implies the existence of a limit for the proportion of vertices covered by a maximum matching. We provide a characterization of the limiting parameter via a local recursion defined directly on the limit of the graph sequence. Interestingly, the recursion may admit multiple solutions, implying non-trivial long-range dependencies between the covered vertices. We overcome this lack of correlation decay by introducing a perturbative parameter (temperature), which we let progressively go to zero. This allows us to uniquely identify the correct solution. In the important case where the graph limit is a unimodular Galton-Watson tree, the recursion simplifies into a distributional equation that can be solved explicitly, leading to a new asymptotic formula that considerably extends the well-known one by Karp and Sipser for Erd\"os-R\'enyi random graphs.Comment: 23 page

Forbidden Induced Subgraphs and the Price of Connectivity for Feedback Vertex Set

Let fvs(G) and cfvs(G) denote the cardinalities of a minimum feedback vertex set and a minimum connected feedback vertex set of a graph G, respectively. For a graph class G, the price of connectivity for feedback vertex set (poc-fvs) for G is defined as the maximum ratio cfvs(G)/fvs(G) over all connected graphs G in G. It is known that the poc-fvs for general graphs is unbounded. We study the poc-fvs for graph classes defined by a finite family H of forbidden induced subgraphs. We characterize exactly those finite families H for which the poc-fvs for H-free graphs is bounded by a constant. Prior to our work, such a result was only known for the case where |H|=1

Exact Weight Subgraphs and the k-Sum Conjecture

We consider the Exact-Weight-H problem of finding a (not necessarily induced) subgraph H of weight 0 in an edge-weighted graph G. We show that for every H, the complexity of this problem is strongly related to that of the infamous k-Sum problem. In particular, we show that under the k-Sum Conjecture, we can achieve tight upper and lower bounds for the Exact-Weight-H problem for various subgraphs H such as matching, star, path, and cycle. One interesting consequence is that improving on the O(n^3) upper bound for Exact-Weight-4-Path or Exact-Weight-5-Path will imply improved algorithms for 3-Sum, 5-Sum, All-Pairs Shortest Paths and other fundamental problems. This is in sharp contrast to the minimum-weight and (unweighted) detection versions, which can be solved easily in time O(n^2). We also show that a faster algorithm for any of the following three problems would yield faster algorithms for the others: 3-Sum, Exact-Weight-3-Matching, and Exact-Weight-3-Star

FRESH: Fréchet similarity with hashing

This paper studies the r-range search problem for curves under the continuous Fréchet distance: given a dataset S of n polygonal curves and a threshold >0 , construct a data structure that, for any query curve q, efficiently returns all entries in S with distance at most r from q. We propose FRESH, an approximate and randomized approach for r-range search, that leverages on a locality sensitive hashing scheme for detecting candidate near neighbors of the query curve, and on a subsequent pruning step based on a cascade of curve simplifications. We experimentally compare FRESH to exact and deterministic solutions, and we show that high performance can be reached by suitably relaxing precision and recall

Annotating Relationships between Multiple Mixed-media Digital Objects by Extending Annotea

Annotea provides an annotation protocol to support collaborative Semantic Web-based annotation of digital resources accessible through the Web. It provides a model whereby a user may attach supplementary information to a resource or part of a resource in the form of: either a simple textual comment; a hyperlink to another web page; a local file; or a semantic tag extracted from a formal ontology and controlled vocabulary. Hence, annotations can be used to attach subjective notes, comments, rankings, queries or tags to enable semantic reasoning across web resources. More recently tabbed Browsers and specific annotation tools, allow users to view several resources (e.g., images, video, audio, text, HTML, PDF) simultaneously in order to carry out side-by-side comparisons. In such scenarios, users frequently want to be able to create and annotate a link or relationship between two or more objects or between segments within those objects. For example, a user might want to create a link between a scene in an original film and the corresponding scene in a remake and attach an annotation to that link. Based on past experiences gained from implementing Annotea within different communities in order to enable knowledge capture, this paper describes and compares alternative ways in which the Annotea Schema may be extended for the purpose of annotating links between multiple resources (or segments of resources). It concludes by identifying and recommending an optimum approach which will enhance the power, flexibility and applicability of Annotea in many domains

Ist ein bisschen Deradikalisierung besser als keine? Zur Ausstiegsarbeit mit Rückkehrerinnen und Rückkehrern aus dschihadistischen Gruppen in Deutschland

Zwischen 2013 und 2019 verließen mehr als 1.000 zumeist junge Menschen Deutschland, um sich in Syrien und dem Irak dschihadistischen Gruppen anzuschließen. Die bekannteste von ihnen ist der sogenannte "Islamische Staat", auf dessen Konto in den Jahren 2015 und 2016 auch mehrere Anschläge in Europa gingen. An diesen Terrorakten beteiligten sich zurückgekehrte europäische Dschihadisten. Inzwischen gilt der "Islamische Staat" zwar als weitgehend besiegt und ein knappes Drittel der nach Syrien und Irak Ausgereisten ist wieder zurück in Deutschland. Doch nicht alle dieser Rückkehrerinnen und Rückkehrer sind desillusioniert. Einige hängen nach wie vor islamistischen Ideologien an, fast alle sind zudem traumatisiert. Ein nicht unerheblicher Teil befindet sich in Haft. Es stellt sich die Frage, wie der Sicherheitsbedrohung, die von diesen Rückkehrerinnen und Rückkehrern ausgeht, zu begegnen ist. Deutschland beschreitet dabei unter anderem den Weg der Resozialisierung: Ausstiegs- und Reintegrationsmaßnahmen sollen diesen Personen den Weg zurück in die Gesellschaft ermöglichen. Durchgeführt werden solche Maßnahmen sowohl von staatlichen Programmen, als auch von zivilgesellschaftlichen Trägern. Dieses BICC Working Paper untersucht, wie Fachkräfte solcher Träger dieser Aufgabe nachkommen und welchen Hindernissen sie dabei begegnen. Um dies zu erläutern, stellt das Paper den gesamten Komplex von der Rückreise ehemaliger Dschihadistinnen und Dschihadisten aus dem Konfliktgebiet, über ihre psychische und soziale Wiedereingliederung nach der Ankunft in Deutschland bis zum Abschluss des Ausstiegsprozesses dar und untersucht die Herausforderungen, die sich dabei für soziale Arbeit und Prävention ergeben. Hierzu gehören besondere Aspekte der Fallarbeit wie der Umgang mit Traumatisierungen, die Bedarfe minderjähriger Rückkehrerinnen und Rückkehrer, die Arbeit in Haftanstalten sowie die Aufarbeitung extremistischer Ideologien. Die Untersuchung zeigt, dass Fachkräfte sich ihrer Aufgabe zwar professionell gewachsen sehen, jedoch einigen strukturellen Herausforderungen gegenüberstehen. Diese umfassen etwa zeitlich und finanziell begrenzte Projektförderungen, einen Mangel an therapeutischen Kapazitäten sowie Abstimmungsprobleme mit den Justizbehörden bei der Arbeit mit inhaftierten Rückkehrerinnen und Rückkehrern

Phase II study of weekly oxaliplatin plus infusional fluorouracil and folinic acid (FUFOX regimen) as first-line treatment in metastatic gastric cancer

Oxaliplatin plus fluorouracil/folinic acid (5-FU/FA) every 2 weeks has shown promising activity in advanced gastric cancer. This study assessed the efficacy and safety of weekly oxaliplatin plus 5-FU/FA (FUFOX regimen) in the metastatic setting. Patients with previously untreated metastatic gastric cancer received oxaliplatin (50 mg m−2) plus FA (500 mg m−2, 2-h infusion) followed by 5-FU (2000 mg m−2, 24-h infusion) given on days 1, 8, 15 and 22 of a 5-week cycle. The primary end point of this multicentre phase II study was the response rate according to RECIST criteria. A total of 48 patients were enrolled. Median age was 62 years and all patients had metastatic disease, with a median number of three involved organs. The most common treatment-related grade 3/4 adverse events were diarrhoea (17%), deep vein thrombosis (15%), neutropenia (8%), nausea (6%), febrile neutropenia (4%), fatigue (4%), anaemia (4%), tumour bleeding (4%), emesis (2%), cardiac ischaemia (2%) and pneumonia (2%). Grade 1/2 sensory neuropathy occurred in 67% of patients but there were no episodes of grade 3 neuropathy. Intent-to-treat analysis showed a response rate of 54% (95% CI, 39–69%), including two complete responses. At a median follow-up of 18.1 months (range 11.2–26.2 months), median survival is 11.4 months (95% CI, 8.0–14.9 months) and the median time to progression is 6.5 months (95% CI, 3.9–9.2 months). The weekly FUFOX regimen is well tolerated and shows notable activity as first-line treatment in metastatic gastric cancer

Resonant nonlinear magneto-optical effects in atoms

In this article, we review the history, current status, physical mechanisms, experimental methods, and applications of nonlinear magneto-optical effects in atomic vapors. We begin by describing the pioneering work of Macaluso and Corbino over a century ago on linear magneto-optical effects (in which the properties of the medium do not depend on the light power) in the vicinity of atomic resonances, and contrast these effects with various nonlinear magneto-optical phenomena that have been studied both theoretically and experimentally since the late 1960s. In recent years, the field of nonlinear magneto-optics has experienced a revival of interest that has led to a number of developments, including the observation of ultra-narrow (1-Hz) magneto-optical resonances, applications in sensitive magnetometry, nonlinear magneto-optical tomography, and the possibility of a search for parity- and time-reversal-invariance violation in atoms.Comment: 51 pages, 23 figures, to appear in Rev. Mod. Phys. in Oct. 2002, Figure added, typos corrected, text edited for clarit

A Perfect Parallel Dictionary

We describe new randomized parallel algorithms for the problems of interval allocation, construction of static dictionaries, and maintenance of dynamic dictionaries. All of our algorithms run optimally in constant time with high probability. Our main result is the construction of what we call a \emph{perfect dictionary}, a scheme that allows $p$ processors implementing a set $M$ in space proportional to $|M|$ to process batches of $p$ \emph{insert}, \emph{delete}, and \emph{lookup} instructions on $M$ in constant time per batch. Our best results are obtained for a new variant of the CRCW PRAM model of computation called the OR PRAM. For other variants of the CRCW PRAM we show slightly weaker results, with some resource bounds increased by a factor of $\Theta(\log^k n)$, where k\in\IN is fixed but arbitrarily large