The benefits of coding over routing in a randomized setting

A novel randomized network coding approach for robust, distributed transmission and compression of information in networks is presented, and its advantages over routing-based approaches is demonstrated

Byzantine modification detection in multicast networks using randomized network coding

Distributed randomized network coding, a robust approach to multicasting in distributed network settings, can be extended to provide Byzantine modification detection without the use of cryptographic functions is presented in this paper

Byzantine Modification Detection in Multicast Networks With Random Network Coding

An information-theoretic approach for detecting Byzantine or adversarial modifications in networks employing random linear network coding is described. Each exogenous source packet is augmented with a flexible number of hash symbols that are obtained as a polynomial function of the data symbols. This approach depends only on the adversary not knowing the random coding coefficients of all other packets received by the sink nodes when designing its adversarial packets. We show how the detection probability varies with the overhead (ratio of hash to data symbols), coding field size, and the amount of information unknown to the adversary about the random code

Minimum-cost multicast over coded packet networks

We consider the problem of establishing minimum-cost multicast connections over coded packet networks, i.e., packet networks where the contents of outgoing packets are arbitrary, causal functions of the contents of received packets. We consider both wireline and wireless packet networks as well as both static multicast (where membership of the multicast group remains constant for the duration of the connection) and dynamic multicast (where membership of the multicast group changes in time, with nodes joining and leaving the group). For static multicast, we reduce the problem to a polynomial-time solvable optimization problem, and we present decentralized algorithms for solving it. These algorithms, when coupled with existing decentralized schemes for constructing network codes, yield a fully decentralized approach for achieving minimum-cost multicast. By contrast, establishing minimum-cost static multicast connections over routed packet networks is a very difficult problem even using centralized computation, except in the special cases of unicast and broadcast connections. For dynamic multicast, we reduce the problem to a dynamic programming problem and apply the theory of dynamic programming to suggest how it may be solved

The vanishing ideal of a finite set of points with multiplicity structures

Given a finite set of arbitrarily distributed points in affine space with arbitrary multiplicity structures, we present an algorithm to compute the reduced Groebner basis of the vanishing ideal under the lexicographic ordering. Our method discloses the essential geometric connection between the relative position of the points with multiplicity structures and the quotient basis of the vanishing ideal, so we will explicitly know the set of leading terms of elements of I. We split the problem into several smaller ones which can be solved by induction over variables and then use our new algorithm for intersection of ideals to compute the result of the original problem. The new algorithm for intersection of ideals is mainly based on the Extended Euclidean Algorithm.Comment: 12 pages,12 figures,ASCM 201

Practical Random Linear Network Coding on GPUs

Abstract. Recently, random linear network coding has been widely applied in peer-to-peer network applications. Instead of sharing the raw data with each other, peers in the network produce and send encoded data to each other. As a result, the communication protocols have been greatly simplified, and the appli-cations experience higher end-to-end throughput and better robustness to net-work churns. Since it is difficult to verify the integrity of the encoded data, such systems can suffer from the famous pollution attack, in which a malicious node can send bad encoded blocks that consist of bogus data. Consequently, the bogus data will be propagated into the whole network at an exponential rate. Homomorphic hash functions (HHFs) have been designed to defend systems from such pollution attacks, but with a new challenge: HHFs require that network coding must be performed in GF(q), where q is a very large prime number. This greatly increases the computational cost of network coding, in ad-dition to the already computational expensive HHFs. This paper exploits the po-tential of the huge computing power of Graphic Processing Units (GPUs) to reduce the computational cost of network coding and homomorphic hashing. With our network coding and HHF implementation on GPU, we observed significant computational speedup in comparison with the best CPU implemen-tation. This implementation can lead to a practical solution for defending the pollution attacks in distributed systems

On the exactness of the cavity method for Weighted b-Matchings on Arbitrary Graphs and its Relation to Linear Programs

We consider the general problem of finding the minimum weight b-matching on arbitrary graphs. We prove that, whenever the linear programming relaxation of the problem has no fractional solutions, then the cavity or belief propagation equations converge to the correct solution both for synchronous and asynchronous updating

Linking Genotype and Phenotype of Saccharomyces cerevisiae Strains Reveals Metabolic Engineering Targets and Leads to Triterpene Hyper-Producers

Background: Metabolic engineering is an attractive approach in order to improve the microbial production of drugs. Triterpenes is a chemically diverse class of compounds and many among them are of interest from a human health perspective. A systematic experimental or computational survey of all feasible gene modifications to determine the genotype yielding the optimal triterpene production phenotype is a laborious and time-consuming process. Methodology/Principal Findings: Based on the recent genome-wide sequencing of Saccharomyces cerevisiae CEN.PK 113-7D and its phenotypic differences with the S288C strain, we implemented a strategy for the construction of a beta-amyrin production platform. The genes Erg8, Erg9 and HFA1 contained non-silent SNPs that were computationally analyzed to evaluate the changes that cause in the respective protein structures. Subsequently, Erg8, Erg9 and HFA1 were correlated with the increased levels of ergosterol and fatty acids in CEN.PK 113-7D and single, double, and triple gene over-expression strains were constructed. Conclusions: The six out of seven gene over-expression constructs had a considerable impact on both ergosterol and beta-amyrin production. In the case of beta-amyrin formation the triple over-expression construct exhibited a nearly 500% increase over the control strain making our metabolic engineering strategy the most successful design of triterpene microbial producers