Abstract. This technical report demonstrates theoretically and empirically that a greedy algorithm called Orthogonal Matching Pursuit (OMP) can reliably recover a signal with m nonzero entries in dimension d given O(m ln d) random linear measurements of that signal. This is a massive improvement over previous results for OMP, which require O(m 2) measurements. The new results for OMP are comparable with recent results for another algorithm called Basis Pursuit (BP). The OMP algorithm is faster and easier to implement, which makes it an attractive alternative to BP for signal recovery problems. 1.

Abstract. We identify and fill some gaps with regard to consistency (the extent to which false positives are produced) for public-key encryption with keyword search (PEKS). We define computational and statistical relaxations of the existing notion of perfect consistency, show that the scheme of [7] is computationally consistent, and provide a new scheme that is statistically consistent. We also provide a transform of an anonymous IBE scheme to a secure PEKS scheme that, unlike the previous one, guarantees consistency. Finally we suggest three extensions of the basic notions considered here, namely anonymous HIBE, public-key encryption with temporary keyword search, and identity-based encryption

A Compressive Sensing Microarray (CSM) is a new device for DNA-based identification of target organisms that leverages the nascent theory of Compressive Sensing (CS). In contrast to a conventional DNA microarray, in which each genetic sensor spot is designed to respond to a single target organism, in a CSM each sensor spot responds to a group of targets. As a result, significantly fewer total sensor spots are required. In this paper, we study how to design group identifier probes that simultaneously account for both the constraints from the CS theory and the biochemistry of probe-target DNA hybridization. We employ Belief Propagation as a CS recovery method to estimate target concentrations from the microarray intensities.

We introduce novel techniques for organizing the indexing structures of how data is stored so that alterations from an original version can be detected and the changed values specifically identified. We give forensic constructions for several fundamental data structures, including arrays, linked lists, binary search trees, skip lists, and hash tables. Some of our constructions are based on a new reduced-randomness construction for nonadaptive combinatorial group testing.

Ding-Zhu Du We propose two new classes of non-adaptive pooling designs. The first one is guaranteed to be ¡-error-detecting ¢¤£¥§ ¦ and thus ¡-error-correcting, where, a positive integer, is the maximum number of defectives (or positives). Hence, the number of errors which can be detected grows linearly with the number of positives. Also, this construction induces a construction of a binary code with minimum Hamming distance ¨ ¨ at least. The second design � is the-analogue of a known construction on ¡-disjunct matrices. 1

We propose a signal recovery method using Belief Propagation (BP) for nonlinear Compressed Sensing (CS) and demonstrate its utility in DNA array decoding. In a CS DNA microarray, the array spots identify DNA sequences that are shared between multiple organisms, thereby reducing the number of spots required. The sparsity in DNA sequence commonality between different organisms translates to conditions that render Belief Propagation (BP) efficient for signal reconstruction. However, an excessively high concentration of target DNA molecules has a nonlinear effect on the measurements — it causes saturation in the measurement intensities at the array spots. We use a modified BP to estimate the target signal coefficients since it is flexible to handle the nonlinearity unlike ℓ1 decoding or other greedy algorithms and show that the original signal coefficients can be recovered from saturated measurements of their linear combinations.

This paper proposes a service-oriented software reliability model that dynamically evaluates the reliability of Web services. There are two kinds of Web services: atomic services without the structural information and the composite services consisting of atomic services. The model first evaluates the reliability of atomic services based on group testing and majority voting. Group testing is the key technique proposed in this paper to support the service-oriented reliability model. Then, the reliability model evaluates the overall reliability of composite services using an architecture-based model and based on reliabilities of the atomic services, execution scenarios, and operational profiles. The reliability model is dynamic and the reliabilities of the services are evaluated in the actual operational environment. A case study is designed, implemented, and analyzed using the design of experiment technique. The results show the significances of the model and its components.

We consider the problem of deterministic distributed coloring of an n-vertex graph with maximum degree \Delta, assuming that every vertex knows a priori only its own label and parameters n and \Delta. The aim is to get a fast algorithm using few colors. Linial [9] showed a vertex-coloring algorithm working in time O(log n) and using O(\Delta 2 ) colors. We improve both the time and the number of colors simultaneously by showing an algorithm working in time O(log (n=\Delta)) and using O(\Delta) colors. This is the first known O(\Delta)-vertex-coloring distributed algorithm which can work faster than in polylogarithmic time. Our method also gives an edge-coloring algorithm with the number of colors and time as above. On the other hand, it follows from Linial [9] that our time of O(\Delta)-coloring cannot be improved in general. 1

Abstract. We propose a family of novel schemes based on Chord retaining all positive aspects that made Chord a popular topology for routing in P2P networks. The schemes, based on the Fibonacci number system, allow to improve on the maximum/average number of hops for lookups and the routing table size per node. 1

We introduce a probabilistic variant of the Guessing Secrets problem proposed by Chung et al. in [2]. In our variation, a player tries to discover the identity of a set S of n unknown secrets drawn by a second player, from a space of N secrets. The rst player tries to learn as much as possible about the elements of S by asking binary questions. For each question asked, the second player randomly chooses one of the n secrets of S that he uses in supplying the answer, which in any case must be truthful. We de ne a simple probabilistic guessing algorithm that allows us to guess all secrets of S with probability one. We show that the expected number of questions needed to guess all secrets is 2n log 2 N and the expected time complexity of the algorithm is O(n log N ). We also propose a generalization of this probabilistic guessing secrets problem, and provide some similar results for this generalization. 1