Related papers: Asynchronous Merkle Trees
In this paper, we extend the notion of a merge tree to that of a generalized merge tree, a merge tree that includes 1-dimensional cycle birth information. Given a discrete Morse function on a $1$-dimensional regular CW complex, we construct…
Blockchain technologies are facing a scalability challenge, which must be overcome to guarantee a wider adoption of the technology. This scalability issue is due to the use of consensus algorithms to guarantee the total order of the chain…
Networks are composed of logical nodes and edges for communications. The atomistic component of things connected to the network is a memory chip. Accordingly, the unique linkage of a memory chip and a logical node can be promising to…
The development of deep learning software libraries enabled significant progress in the field by allowing users to focus on modeling, while letting the library to take care of the tedious and time-consuming task of optimizing execution for…
The design of access control mechanisms for healthcare systems is challenging: it must strike the right balance between permissions and restrictions. In this work, we propose a novel approach that is based on the Blockchain technology for…
Many data are naturally modeled by an unobserved hierarchical structure. In this paper we propose a flexible nonparametric prior over unknown data hierarchies. The approach uses nested stick-breaking processes to allow for trees of…
Integrity of audit logs produced by Internet of Things (IoT) devices is a prerequisite for post-incident forensics, regulatory compliance, and operational accountability. While blockchain-backed logging infrastructures can satisfy this…
Computer power is a constantly increasing demand in scientific data analyses, in particular when Markov Chain Monte Carlo (MCMC) methods are involved, for example for estimating integral functions or Bayesian posterior probabilities. In…
The main problem faced by smart contract platforms is the amount of time and computational power required to reach consensus. In a classical blockchain model, each operation is in fact performed by each node, both to update the status and…
Recent advances in reasoning models have demonstrated significant improvements in accuracy by employing detailed and comprehensive reasoning processes. However, generating these lengthy reasoning sequences is computationally expensive and…
Regression trees are one of the oldest forms of AI models, and their predictions can be made without a calculator, which makes them broadly useful, particularly for high-stakes applications. Within the large literature on regression trees,…
Tree-based models have proven to be an effective solution for web ranking as well as other problems in diverse domains. This paper focuses on optimizing the runtime performance of applying such models to make predictions, given an…
Suffix trees have recently become very successful data structures in handling large data sequences such as DNA or Protein sequences. Consequently parallel architectures have become ubiquitous. We present a novel alphabet-dependent parallel…
Existing parallel algorithms for wavelet tree construction have a work complexity of $O(n\log\sigma)$. This paper presents parallel algorithms for the problem with improved work complexity. Our first algorithm is based on parallel integer…
It is interesting but difficult and challenging to study Ethereum with multiple mining pools. One of the main difficulties comes from not only how to represent such a general tree with multiple block branches (or sub-chains) related to the…
Ordered sets and maps play important roles as index structures in relational data models. When a shared index in a multi-user system is modified concurrently, the current state of the index will diverge into multiple versions containing the…
In this paper, we consider the convergence of a very general asynchronous-parallel algorithm called ARock, that takes many well-known asynchronous algorithms as special cases (gradient descent, proximal gradient, Douglas Rachford, ADMM,…
We congratulate Lee, Nadler and Wasserman (henceforth LNW) on a very interesting paper on new methodology and supporting theory [arXiv:0707.0481]. Treelets seem to tackle two important problems of modern data analysis at once. For datasets…
Emerging applications of blockchains, such as grocery supply chains, require frequent updates to the data structure. This is in contrast with typical analyses of the Bitcoin blockchain, in which updates occur infrequently. With more…
In this paper we consider two aspects of the inverse problem of how to construct merge trees realizing a given barcode. Much of our investigation exploits a recently discovered connection between the symmetric group and barcodes in general…