Deterministic Coupon Collection and Better Strong Dispersers

Hashing is one of the main techniques in data processing and algorithm design for very large data sets. While random hash functions satisfy most desirable properties, it is often too expensive to store a fully random hash function. Motivated by this, much attention has been given to designing small families of hash functions suitable for various applications. In this work, we study the question of designing space-efficient hash families H = {h:[U] -> [N]} with the natural property of \u27covering\u27: H is said to be covering if any set of Omega(N log N) distinct items from the universe (the "coupon-collector limit") are hashed to cover all N bins by most hash functions in H. We give an explicit covering family H of size poly(N) (which is optimal), so that hash functions in H can be specified efficiently by O(log N) bits. We build covering hash functions by drawing a connection to "dispersers", which are quite well-studied and have a variety of applications themselves. We in fact need strong dispersers and we give new constructions of strong dispersers which may be of independent interest. Specifically, we construct strong dispersers with optimal entropy loss in the high min-entropy, but very small error (poly(n)/2^n for n bit sources) regimes. We also provide a strong disperser construction with constant error but for any min-entropy. Our constructions achieve these by using part of the source to replace seed from previous non-strong constructions in surprising ways. In doing so, we take two of the few constructions of dispersers with parameters better than known extractors and make them strong

Information Gathering in Ad-Hoc Radio Networks with Tree Topology

We study the problem of information gathering in ad-hoc radio networks without collision detection, focussing on the case when the network forms a tree, with edges directed towards the root. Initially, each node has a piece of information that we refer to as a rumor. Our goal is to design protocols that deliver all rumors to the root of the tree as quickly as possible. The protocol must complete this task within its allotted time even though the actual tree topology is unknown when the computation starts. In the deterministic case, assuming that the nodes are labeled with small integers, we give an O(n)-time protocol that uses unbounded messages, and an O(n log n)-time protocol using bounded messages, where any message can include only one rumor. We also consider fire-and-forward protocols, in which a node can only transmit its own rumor or the rumor received in the previous step. We give a deterministic fire-and- forward protocol with running time O(n^1.5), and we show that it is asymptotically optimal. We then study randomized algorithms where the nodes are not labelled. In this model, we give an O(n log n)-time protocol and we prove that this bound is asymptotically optimal

Memoryless Worker-Task Assignment with Polylogarithmic Switching Cost

We study the basic problem of assigning memoryless workers to tasks with dynamically changing demands. Given a set of $w$ workers and a multiset $T \subseteq[t]$ of $|T|=w$ tasks, a memoryless worker-task assignment function is any function $\phi$ that assigns the workers $[w]$ to the tasks $T$ based only on the current value of $T$. The assignment function $\phi$ is said to have switching cost at most $k$ if, for every task multiset $T$, changing the contents of $T$ by one task changes $\phi(T)$ by at most $k$ worker assignments. The goal of memoryless worker task assignment is to construct an assignment function with the smallest possible switching cost. In past work, the problem of determining the optimal switching cost has been posed as an open question. There are no known sub-linear upper bounds, and after considerable effort, the best known lower bound remains 4 (ICALP 2020). We show that it is possible to achieve polylogarithmic switching cost. We give a construction via the probabilistic method that achieves switching cost $O(\log w \log (wt))$ and an explicit construction that achieves switching cost $\operatorname{polylog} (wt)$. We also prove a super-constant lower bound on switching cost: we show that for any value of $w$, there exists a value of $t$ for which the optimal switching cost is $w$. Thus it is not possible to achieve a switching cost that is sublinear strictly as a function of $w$. Finally, we present an application of the worker-task assignment problem to a metric embeddings problem. In particular, we use our results to give the first low-distortion embedding from sparse binary vectors into low-dimensional Hamming space.Comment: ICALP 202

Using and saving randomness

Randomness is ubiquitous and exceedingly useful in computer science. For example, in sparse recovery, randomized algorithms are more efficient and robust than their deterministic counterparts. At the same time, because random sources from the real world are often biased and defective with limited entropy, high-quality randomness is a precious resource. This motivates the studies of pseudorandomness and randomness extraction. In this thesis, we explore the role of randomness in these areas. Our research contributions broadly fall into two categories: learning structured signals and constructing pseudorandom objects. Learning a structured signal. One common task in audio signal processing is to compress an interval of observation through finding the dominating k frequencies in its Fourier transform. We study the problem of learning a Fourier-sparse signal from noisy samples, where [0, T] is the observation interval and the frequencies can be “off-grid”. Previous methods for this problem required the gap between frequencies to be above 1/T, which is necessary to robustly identify individual frequencies. We show that this gap is not necessary to recover the signal as a whole: for arbitrary k-Fourier-sparse signals under ℓ₂ bounded noise, we provide a learning algorithm with a constant factor growth of the noise and sample complexity polynomial in k and logarithmic in the bandwidth and signal-to-noise ratio. In addition to this, we introduce a general method to avoid a condition number depending on the signal family F and the distribution D of measurement in the sample vi complexity. In particular, for any linear family F with dimension d and any distribution D over the domain of F, we show that this method provides a robust learning algorithm with O(d log d) samples. Furthermore, we improve the sample complexity to O(d) via spectral sparsification (optimal up to a constant factor), which provides the best known result for a range of linear families such as low degree multivariate polynomials. Next, we generalize this result to an active learning setting, where we get a large number of unlabeled points from an unknown distribution and choose a small subset to label. We design a learning algorithm optimizing both the number of unlabeled points and the number of labels. Pseudorandomness. Next, we study hash families, which have simple forms in theory and efficient implementations in practice. The size of a hash family is crucial for many applications such as derandomization. In this thesis, we study the upper bound on the size of hash families to fulfill their applications in various problems. We first investigate the number of hash functions to constitute a randomness extractor, which is equivalent to the degree of the extractor. We present a general probabilistic method that reduces the degree of any given strong extractor to almost optimal, at least when outputting few bits. For various almost universal hash families including Toeplitz matrices, Linear Congruential Hash, and Multiplicative Universal Hash, this approach significantly improves the upper bound on the degree of strong extractors in these hash families. Then we consider explicit hash families and multiple-choice schemes in the classical problems of placing balls into bins. We construct explicit hash families of almost-polynomial size that derandomizes two classical multiple-choice schemes, which match the maximum loads of a perfectly random hash function.Computer Science

Bounded Collusion Protocols, Cylinder-Intersection Extractors and Leakage-Resilient Secret Sharing

In this work we study bounded collusion protocols (BCPs) recently introduced in the context of secret sharing by Kumar, Meka, and Sahai (FOCS 2019). These are multi-party communication protocols on $n$ parties where in each round a subset of $p$-parties (the collusion bound) collude together and write a function of their inputs on a public blackboard. BCPs interpolate elegantly between the well-studied number-in-hand (NIH) model ($p=1$) and the number-on-forehead (NOF) model ($p=n-1$). Motivated by questions in communication complexity, secret sharing, and pseudorandomness we investigate BCPs more thoroughly, answering several questions about them. * We prove a polynomial (in the input-length) lower bound for an explicit function against BCPs where any constant fraction of players can collude. Previously, nontrivial lower bounds were known only when the collusion bound was at most logarithmic in the input-length (owing to bottlenecks in NOF lower bounds). * For all $t \leq n$, we construct efficient $t$-out-of-$n$ secret sharing schemes where the secret remains hidden even given the transcript of a BCP with collusion bound $O(t/\log t)$. Prior work could only handle collusions of size $O(\log n)$. Along the way, we construct leakage-resilient schemes against disjoint and adaptive leakage, resolving a question asked by Goyal and Kumar (STOC 2018). * An explicit $n$-source cylinder intersection extractor whose output is close to uniform even when given the transcript of a BCP with a constant fraction of parties colluding. The min-entropy rate we require is $0.3$ (independent of collusion bound $p \ll n$). Our results rely on a new class of exponential sums that interpolate between the ones considered in additive combinatorics by Bourgain (Geometric and Functional Analysis 2009) and Petridis and Shparlinski (Journal d\u27Analyse Mathématique 2019)

Notes on Randomized Algorithms

Lecture notes for the Yale Computer Science course CPSC 469/569 Randomized Algorithms. Suitable for use as a supplementary text for an introductory graduate or advanced undergraduate course on randomized algorithms. Discusses tools from probability theory, including random variables and expectations, union bound arguments, concentration bounds, applications of martingales and Markov chains, and the Lov\'asz Local Lemma. Algorithmic topics include analysis of classic randomized algorithms such as Quicksort and Hoare's FIND, randomized tree data structures, hashing, Markov chain Monte Carlo sampling, randomized approximate counting, derandomization, quantum computing, and some examples of randomized distributed algorithms

Planning, Nature and Ecosystem Services

This book collects the papers presented at INPUT aCAdemy 2019, a special edition of the INPUT Conference hosted by the Department of Civil and Environmental Engineering, and Architecture (DICAAR) of the University of Cagliari. INPUT aCAdemy Conference will focus on contemporary planning issues with particular attention to ecosystem services, green and blue infrastructure and governance and management of Natura 2000 sites and coastal marine areas. INPUT aCAdemy 2019 is organized within the GIREPAM Project (Integrated Management of Ecological Networks through Parks and Marine Areas), co-funded by the European Regional Development Fund (ERDF) in relation to the 2014-2020 Interreg Italy – France (Maritime) Programme. INPUT aCAdemy 2019 is supported by Società Italiana degli Urbanisti (SIU, the Italian Society of Spatial Planners), Istituto Nazionale di Urbanistica (INU, the Italian National Institute of Urban Planning), UrbIng Ricerca Scientifica (the Association of Spatial Planning Scholars of the Italian Schools of Engineering) and Ordine degli Ingegneri di Cagliari (OIC, Professional Association of Engineers of Cagliari).illustratorThis book collects the papers presented at INPUT aCAdemy 2019, a special edition of the INPUT Conference hosted by the Department of Civil and Environmental Engineering, and Architecture (DICAAR) of the University of Cagliari. INPUT aCAdemy Conference will focus on contemporary planning issues with particular attention to ecosystem services, green and blue infrastructure and governance and management of Natura 2000 sites and coastal marine areas. INPUT aCAdemy 2019 is organized within the GIREPAM Project (Integrated Management of Ecological Networks through Parks and Marine Areas), co-funded by the European Regional Development Fund (ERDF) in relation to the 2014-2020 Interreg Italy – France (Maritime) Programme. INPUT aCAdemy 2019 is supported by Società Italiana degli Urbanisti (SIU, the Italian Society of Spatial Planners), Istituto Nazionale di Urbanistica (INU, the Italian National Institute of Urban Planning), UrbIng Ricerca Scientifica (the Association of Spatial Planning Scholars of the Italian Schools of Engineering) and Ordine degli Ingegneri di Cagliari (OIC, Professional Association of Engineers of Cagliari)

Sustainable agriculture and rural development in terms of the republic of Serbia strategic goals realization within the Danube region. Achieving regional competitiveness

International Scientific Conference „SUSTAINABLE AGRICULTURE AND RURAL DEVELOPMENT IN TERMS OF THE REPUBLIC OF SERBIA STRATEGIC GOALS REALIZATION WITHIN THE DANUBE REGION -achieving regional competitiveness“, which was held in period 5-7th December 2013 in Topola, the Republic of Serbia, through number of presented papers mainly provides an overview of results of scientific research on the integrated and interdisciplinary project no. III 46006 „SUSTAINABLE AGRICULTURE AND RURAL DEVELOPMENT IN TERMS OF THE REPUBLIC OF SERBIA STRATEGIC GOALS REALIZATION WITHIN THE DANUBE REGION“. International Scientific Conference „SUSTAINABLE AGRICULTURE AND RURAL DEVELOPMENT IN TERMS OF THE REPUBLIC OF SERBIA STRATEGIC GOALS REALIZATION WITHIN THE DANUBE REGION - achieving regional competitiveness“, gathered number of scientific workers and experts from many countries. Besides the authors from Serbia in Thematic Proceedings are also presented the papers of authors from Bosnia and Herzegovina, Macedonia, Romania, Russia, Moldova, Slovakia, Ukraine, Germany, the Netherlands, Japan and Austria. After all 92 papers were positively reviewed by the reviewers and presented on the International Scientific Conference, they were published in the Thematic Proceedings. Proceedings publisher was Institute of Agricultural Economics Belgrade, together with 34 eminent scientific-educational institutions from Serbia and abroad. In the Plenary Section were presented 3 papers which gave significant contributions to International Scientific Conference. Rest of the papers are systematized in 3 thematic sections: IKNOWLEDGE ECONOMY AND HUMAN CAPITAL IN THE FUNCTION OF IMPROVING REGIONAL COMPETITIVENESS (45 papers); II BIOREGIONALISM AND PERMACULTURE AS A CONCEPTS OF CONSERVATION OF ECOLOGICAL SPECIFICITIES OF RURAL AREAS (27 papers); III THE CONSTRUCTION OF AGRO-REGIONAL IDENTITY THROUGH INSTITUTIONAL REFORM (17 papers)

Sustainable agriculture and rural development in terms of the republic of Serbia strategic goals realization within the Danube region. Achieving regional competitiveness

International Scientific Conference „SUSTAINABLE AGRICULTURE AND RURAL DEVELOPMENT IN TERMS OF THE REPUBLIC OF SERBIA STRATEGIC GOALS REALIZATION WITHIN THE DANUBE REGION -achieving regional competitiveness“, which was held in period 5-7th December 2013 in Topola, the Republic of Serbia, through number of presented papers mainly provides an overview of results of scientific research on the integrated and interdisciplinary project no. III 46006 „SUSTAINABLE AGRICULTURE AND RURAL DEVELOPMENT IN TERMS OF THE REPUBLIC OF SERBIA STRATEGIC GOALS REALIZATION WITHIN THE DANUBE REGION“. International Scientific Conference „SUSTAINABLE AGRICULTURE AND RURAL DEVELOPMENT IN TERMS OF THE REPUBLIC OF SERBIA STRATEGIC GOALS REALIZATION WITHIN THE DANUBE REGION - achieving regional competitiveness“, gathered number of scientific workers and experts from many countries. Besides the authors from Serbia in Thematic Proceedings are also presented the papers of authors from Bosnia and Herzegovina, Macedonia, Romania, Russia, Moldova, Slovakia, Ukraine, Germany, the Netherlands, Japan and Austria. After all 92 papers were positively reviewed by the reviewers and presented on the International Scientific Conference, they were published in the Thematic Proceedings. Proceedings publisher was Institute of Agricultural Economics Belgrade, together with 34 eminent scientific-educational institutions from Serbia and abroad. In the Plenary Section were presented 3 papers which gave significant contributions to International Scientific Conference. Rest of the papers are systematized in 3 thematic sections: IKNOWLEDGE ECONOMY AND HUMAN CAPITAL IN THE FUNCTION OF IMPROVING REGIONAL COMPETITIVENESS (45 papers); II BIOREGIONALISM AND PERMACULTURE AS A CONCEPTS OF CONSERVATION OF ECOLOGICAL SPECIFICITIES OF RURAL AREAS (27 papers); III THE CONSTRUCTION OF AGRO-REGIONAL IDENTITY THROUGH INSTITUTIONAL REFORM (17 papers)