GROTESQUE: Noisy Group Testing (Quick and Efficient)

Group-testing refers to the problem of identifying (with high probability) a (small) subset of $D$ defectives from a (large) set of $N$ items via a "small" number of "pooled" tests. For ease of presentation in this work we focus on the regime when D = \cO{N^{1-\gap}} for some \gap > 0. The tests may be noiseless or noisy, and the testing procedure may be adaptive (the pool defining a test may depend on the outcome of a previous test), or non-adaptive (each test is performed independent of the outcome of other tests). A rich body of literature demonstrates that $\Theta(D\log(N))$ tests are information-theoretically necessary and sufficient for the group-testing problem, and provides algorithms that achieve this performance. However, it is only recently that reconstruction algorithms with computational complexity that is sub-linear in $N$ have started being investigated (recent work by \cite{GurI:04,IndN:10, NgoP:11} gave some of the first such algorithms). In the scenario with adaptive tests with noisy outcomes, we present the first scheme that is simultaneously order-optimal (up to small constant factors) in both the number of tests and the decoding complexity (\cO{D\log(N)} in both the performance metrics). The total number of stages of our adaptive algorithm is "small" (\cO{\log(D)}). Similarly, in the scenario with non-adaptive tests with noisy outcomes, we present the first scheme that is simultaneously near-optimal in both the number of tests and the decoding complexity (via an algorithm that requires \cO{D\log(D)\log(N)} tests and has a decoding complexity of {${\cal O}(D(\log N+\log^{2}D))$}. Finally, we present an adaptive algorithm that only requires 2 stages, and for which both the number of tests and the decoding complexity scale as {${\cal O}(D(\log N+\log^{2}D))$}. For all three settings the probability of error of our algorithms scales as \cO{1/(poly(D)}.Comment: 26 pages, 5 figure

Signal Recovery from Pooling Representations

In this work we compute lower Lipschitz bounds of $\ell_p$ pooling operators for $p=1, 2, \infty$ as well as $\ell_p$ pooling operators preceded by half-rectification layers. These give sufficient conditions for the design of invertible neural network layers. Numerical experiments on MNIST and image patches confirm that pooling layers can be inverted with phase recovery algorithms. Moreover, the regularity of the inverse pooling, controlled by the lower Lipschitz constant, is empirically verified with a nearest neighbor regression.Comment: 17 pages, 3 figure

Performance of IP address auto-configuration protocols in Delay and Disruptive Tolerant Networks

At this moment there is a lack of research respecting Mobile Ad-hoc Networks (MANET) address assignment methods used in Delay Tolerant Networks (DTN). The goal of this paper is to review the SDAD, WDAD and Buddy methods of IP address assignment known from MANET in difficult environment of Delay and Disruptive Tolerant Networks. Our research allows us for estimating the effectiveness of the chosen solution and, therefore, to choose the most suitable one for specified conditions. As a part of the work we have created a tool which allows to compare these methods in terms of capability of solving address conflicts and network load. Our simulator was created from scratch in Java programming language in such a manner, that implementation of new features and improvements in the future will be as convenient as possible

Evaluating Automatic Pools Distribution Techniques for Self-Configured Networks

NextGeneration of Networks (NGN) is one of the most important research topics of the last decade. Current Internet is not capable of supporting new users and operators’ demands and a new structure will be necessary to them. In this context many solutions might be necessary: from architectural definitions to new protocols. Addressing protocols are a specific example of protocols which should be defined to support NGN requirements. One special required characteristic is automation of addresses assignment to facilitate networks operation and design. Many addressing levels can be considered, however, proposed solutions are usually restricted to local networks addresses distribution. In this paper we present an analysis over automatic address distribution to networks, allowing a correct local addresses’ assignment. Two allocation techniques are presented and evaluated to present the benefits of this kind of mechanisms. Finally, conclusions about the proposed methodologies and the protocols applicability are discussed

Ad Hoc Networking in the Internet: A Deeper Problem Than It Seems

Self-organized networks, also known as ad hoc networks or MANETs, are expected to soon become important components in the Internet architecture. Numerous efforts currently focus on the accomplishment of scalable and efficient mobile ad hoc routing, an essential piece in order to fully integrate ad hoc networks in the Internet. However, an orthogonal and yet as important issue lies with ad hoc IP autoconfiguration. Indeed, prior to participation in IP communication and routing, a node must acquire IP addresse(s) to configure its interface(s). These IP addresses may be required to be unique within a certain scope and/or topologically "correct". Since nodes may be mobile and neither the set of nodes in the MANET nor their connections to each other is pre-determined, the proper configuration must be detected and acquired automatically. This paper reviews the applicability, in the particular context of MANETs, of standard automatic address configuration and prefix allocation protocols, and identifies the different categories of issues that are not solved by these protocols. The paper then elaborates further on why these issues are more profound than they seem, as they pertain to graph theory and are in fact real scalability and architectural issues for the Internet of tomorrow