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Thomas Sauerwald

Bio: Thomas Sauerwald is an academic researcher from University of Cambridge. The author has contributed to research in topics: Random walk & Random graph. The author has an hindex of 30, co-authored 120 publications receiving 2373 citations. Previous affiliations of Thomas Sauerwald include Simon Fraser University & University of Paderborn.


Papers
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Proceedings ArticleDOI
20 Jan 2008
TL;DR: A quasirandom analogue to the classical push model for disseminating information in networks ("randomized rumor spreading") that achieves similar or better broadcasting times with a greatly reduced use of random bits.
Abstract: We propose and analyse a quasirandom analogue to the classical push model for disseminating information in networks ("randomized rumor spreading"). In the classical model, in each round each informed node chooses a neighbor at random and informs it. Results of Frieze and Grimmett (Discrete Appl. Math. 1985) show that this simple protocol succeeds in spreading a rumor from one node of a complete graph to all others within O(log n) rounds. For the network being a hypercube or a random graph G(n, p) with p ≥ (1 +e)(log n)/n, also O(log n) rounds suffice (Feige, Peleg. Raghavan, and Upfal, Random Struct. Algorithms 1990). In the quasirandom model, we assume that each node has a (cyclic) list of its neighbors. Once informed, it starts at a random position of the list, but from then on informs its neighbors in the order of the list. Surprisingly, irrespective of the orders of the lists, the above mentioned bounds still hold. In addition, we also show a O(log n) bound for sparsely connected random graphs G(n, p) with p = (log n + f(n))/n, where f(n) → ∞ and f(n) = O(log log n). Here, the classical model needs Θ(log2(n)) rounds. Hence the quasirandom model achieves similar or better broadcasting times with a greatly reduced use of random bits.

98 citations

Journal ArticleDOI
TL;DR: Besides proving that BUBBLE-FOS/C converges towards a local optimum, this paper develops a much faster method for the improvement of partitionings, based on a different diffusive process, which is restricted to local areas of the graph and also contains a high degree of parallelism.

95 citations

Proceedings ArticleDOI
04 Jun 2011
TL;DR: In this paper, the stabilizing consensus problem is studied and a simple randomized algorithm called median rule is proposed that, with high probability, just needs O(log m log log n + log n) time and work per process to arrive at an almost stable consensus for any set of m legal values as long as an adversary can corrupt the states of at most n processes at any time.
Abstract: In the standard consensus problem there are n processes with possibly different input values and the goal is to eventually reach a point at which all processes commit to exactly one of these values. We are studying a slight variant of the consensus problem called the stabilizing consensus problem [2]. In this problem, we do not require that each process commits to a final value at some point, but that eventually they arrive at a common, stable value without necessarily being aware of that. This should work irrespective of the states in which the processes are starting. Our main result is a simple randomized algorithm called median rule that, with high probability, just needs O(log m log log n + log n) time and work per process to arrive at an almost stable consensus for any set of m legal values as long as an adversary can corrupt the states of at most √n processes at any time. Without adversarial involvement, just O(log n) time and work is needed for a stable consensus, with high probability. As a by-product, we obtain a simple distributed algorithm for approximating the median of n numbers in time O(log m log log n + log n) under adversarial presence.

94 citations

Journal ArticleDOI
TL;DR: The findings reveal a surprisingly sharp threshold behaviour for certain graphs, e.g., the d-dimensional torus with d>2 and hypercubes: there is a value T such that the speed-up is approximately min{T,k} for any 1=2, and the bounds are tight up to logarithmic factors.

94 citations

Proceedings ArticleDOI
17 Jan 2012
TL;DR: Surprisingly, it is able to show that, if 2 < β < 3, the rumor spreads even in constant time, which is much smaller than the typical distance of two nodes, and the first result that establishes a gap between the synchronous and the asynchronous protocol.
Abstract: We analyze the popular push-pull protocol for spreading a rumor in networks. Initially, a single node knows of a rumor. In each succeeding round, every node chooses a random neighbor, and the two nodes share the rumor if one of them is already aware of it. We present the first theoretical analysis of this protocol on random graphs that have a power law degree distribution with an arbitrary exponent β > 2.Our main findings reveal a striking dichotomy in the performance of the protocol that depends on the exponent of the power law. More specifically, we show that if 2 3, then Ω(log n) rounds are necessary.We also investigate the asynchronous version of the push-pull protocol, where the nodes do not operate in rounds, but exchange information according to a Poisson process with rate 1. Surprisingly, we are able to show that, if 2

93 citations


Cited by
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Proceedings ArticleDOI
22 Jan 2006
TL;DR: Some of the major results in random graphs and some of the more challenging open problems are reviewed, including those related to the WWW.
Abstract: We will review some of the major results in random graphs and some of the more challenging open problems. We will cover algorithmic and structural questions. We will touch on newer models, including those related to the WWW.

7,116 citations

Journal Article
TL;DR: In this paper, the coding exons of the family of 518 protein kinases were sequenced in 210 cancers of diverse histological types to explore the nature of the information that will be derived from cancer genome sequencing.
Abstract: AACR Centennial Conference: Translational Cancer Medicine-- Nov 4-8, 2007; Singapore PL02-05 All cancers are due to abnormalities in DNA. The availability of the human genome sequence has led to the proposal that resequencing of cancer genomes will reveal the full complement of somatic mutations and hence all the cancer genes. To explore the nature of the information that will be derived from cancer genome sequencing we have sequenced the coding exons of the family of 518 protein kinases, ~1.3Mb DNA per cancer sample, in 210 cancers of diverse histological types. Despite the screen being directed toward the coding regions of a gene family that has previously been strongly implicated in oncogenesis, the results indicate that the majority of somatic mutations detected are “passengers”. There is considerable variation in the number and pattern of these mutations between individual cancers, indicating substantial diversity of processes of molecular evolution between cancers. The imprints of exogenous mutagenic exposures, mutagenic treatment regimes and DNA repair defects can all be seen in the distinctive mutational signatures of individual cancers. This systematic mutation screen and others have previously yielded a number of cancer genes that are frequently mutated in one or more cancer types and which are now anticancer drug targets (for example BRAF , PIK3CA , and EGFR ). However, detailed analyses of the data from our screen additionally suggest that there exist a large number of additional “driver” mutations which are distributed across a substantial number of genes. It therefore appears that cells may be able to utilise mutations in a large repertoire of potential cancer genes to acquire the neoplastic phenotype. However, many of these genes are employed only infrequently. These findings may have implications for future anticancer drug development.

2,737 citations

Journal ArticleDOI
TL;DR: This handbook is a very useful handbook for engineers, especially those working in signal processing, and provides real data bootstrap applications to illustrate the theory covered in the earlier chapters.
Abstract: tions. Bootstrap has found many applications in engineering field, including artificial neural networks, biomedical engineering, environmental engineering, image processing, and radar and sonar signal processing. Basic concepts of the bootstrap are summarized in each section as a step-by-step algorithm for ease of implementation. Most of the applications are taken from the signal processing literature. The principles of the bootstrap are introduced in Chapter 2. Both the nonparametric and parametric bootstrap procedures are explained. Babu and Singh (1984) have demonstrated that in general, these two procedures behave similarly for pivotal (Studentized) statistics. The fact that the bootstrap is not the solution for all of the problems has been known to statistics community for a long time; however, this fact is rarely touched on in the manuscripts meant for practitioners. It was first observed by Babu (1984) that the bootstrap does not work in the infinite variance case. Bootstrap Techniques for Signal Processing explains the limitations of bootstrap method with an example. I especially liked the presentation style. The basic results are stated without proofs; however, the application of each result is presented as a simple step-by-step process, easy for nonstatisticians to follow. The bootstrap procedures, such as moving block bootstrap for dependent data, along with applications to autoregressive models and for estimation of power spectral density, are also presented in Chapter 2. Signal detection in the presence of noise is generally formulated as a testing of hypothesis problem. Chapter 3 introduces principles of bootstrap hypothesis testing. The topics are introduced with interesting real life examples. Flow charts, typical in engineering literature, are used to aid explanations of the bootstrap hypothesis testing procedures. The bootstrap leads to second-order correction due to pivoting; this improvement in the results due to pivoting is also explained. In the second part of Chapter 3, signal processing is treated as a regression problem. The performance of the bootstrap for matched filters as well as constant false-alarm rate matched filters is also illustrated. Chapters 2 and 3 focus on estimation problems. Chapter 4 introduces bootstrap methods used in model selection. Due to the inherent structure of the subject matter, this chapter may be difficult for nonstatisticians to follow. Chapter 5 is the most impressive chapter in the book, especially from the standpoint of statisticians. It provides real data bootstrap applications to illustrate the theory covered in the earlier chapters. These include applications to optimal sensor placement for knock detection and land-mine detection. The authors also provide a MATLAB toolbox comprising frequently used routines. Overall, this is a very useful handbook for engineers, especially those working in signal processing.

1,292 citations

Journal ArticleDOI
TL;DR: This article designs a blockchain empowered secure data sharing architecture for distributed multiple parties, and incorporates privacy-preserved federated learning in the consensus process of permissioned blockchain, so that the computing work for consensus can also be used for federated training.
Abstract: The rapid increase in the volume of data generated from connected devices in industrial Internet of Things paradigm, opens up new possibilities for enhancing the quality of service for the emerging applications through data sharing. However, security and privacy concerns (e.g., data leakage) are major obstacles for data providers to share their data in wireless networks. The leakage of private data can lead to serious issues beyond financial loss for the providers. In this article, we first design a blockchain empowered secure data sharing architecture for distributed multiple parties. Then, we formulate the data sharing problem into a machine-learning problem by incorporating privacy-preserved federated learning. The privacy of data is well-maintained by sharing the data model instead of revealing the actual data. Finally, we integrate federated learning in the consensus process of permissioned blockchain, so that the computing work for consensus can also be used for federated training. Numerical results derived from real-world datasets show that the proposed data sharing scheme achieves good accuracy, high efficiency, and enhanced security.

668 citations

Journal ArticleDOI

590 citations