Dynamically Adjusting the Mining Capacity in Cryptocurrency with Binary Blockchain

Many cryptocurrencies rely on Blockchain for its operation. Blockchain serves as a public ledger where all the completed transactions can be looked up. To place transactions in the Blockchain, a mining operation must be performed. However, due to a limited mining capacity, the transaction confirmation time is increasing. To mitigate this problem many ideas have been proposed, but they all come with own challenges. We propose a novel parallel mining method that can adjust the mining capacity dynamically depending on the congestion level. It does not require an increase in the block size or a reduction of the block confirmation time. The proposed scheme can increase the number of parallel blockchains when the mining congestion is experienced, which is especially effective under DDoS attack situation. We describe how and when the Blockchain is split or merged, how to solve the imbalanced mining problem, and how to adjust the difficulty levels and rewards. We then show the simulation results comparing the performance of binary blockchain and the traditional single blockchain

Approximate Discrete Probability Distribution Representation using a Multi-ResolutionBinary Tree

Computing and storing probabilities is a hard problem as soon as one has to deal with complex distributions over multiples random variables. The problem of efficient representation of probability distributions is central in term of computational efficiency in the field of probabilistic reasoning. The main problem arises when dealing with joint probability distributions over a set of random variables: they are always represented using huge probability arrays. In this paper, a new method based on a binary-tree representation is introduced in order to store efficiently very large joint distributions. Our approach approximates any multidimensional joint distributions using an adaptive discretization of the space. We make the assumption that the lower is the probability mass of a particular region of feature space, the larger is the discretization step. This assumption leads to a very optimized representation in term of time and memory. The other advantages of our approach are the ability to refine dynamically the distribution every time it is needed leading to a more accurate representation of the probability distribution and to an anytime representation of the distribution

Balancing lists: a proof pearl

Starting with an algorithm to turn lists into full trees which uses non-obvious invariants and partial functions, we progressively encode the invariants in the types of the data, removing most of the burden of a correctness proof. The invariants are encoded using non-uniform inductive types which parallel numerical representations in a style advertised by Okasaki, and a small amount of dependent types.Comment: To appear in proceedings of Interactive Theorem Proving (2014

A New Framework for Join Product Skew

Different types of data skew can result in load imbalance in the context of parallel joins under the shared nothing architecture. We study one important type of skew, join product skew (JPS). A static approach based on frequency classes is proposed which takes for granted the data distribution of join attribute values. It comes from the observation that the join selectivity can be expressed as a sum of products of frequencies of the join attribute values. As a consequence, an appropriate assignment of join sub-tasks, that takes into consideration the magnitude of the frequency products can alleviate the join product skew. Motivated by the aforementioned remark, we propose an algorithm, called Handling Join Product Skew (HJPS), to handle join product skew