Related papers: Noisy Tree Data Structures and Quantum Application…
Fault tree analysis is a technique widely used in risk and reliability analysis of complex engineering systems given its deductive nature and relatively simple interpretation. In a fault tree, events are usually represented by a binary…
Working with tree graphs is always easier than with loopy ones and spanning trees are the closest tree-like structures to a given graph. We find a correspondence between the solutions of random K-satisfiability problem and those of spanning…
One of the key problems in tensor network based quantum circuit simulation is the construction of a contraction tree which minimizes the cost of the simulation, where the cost can be expressed in the number of operations as a proxy for the…
Consider the computations at a node in a message passing algorithm. Assume that the node has incoming and outgoing messages $\mathbf{x} = (x_1, x_2, \ldots, x_n)$ and $\mathbf{y} = (y_1, y_2, \ldots, y_n)$, respectively. In this paper, we…
Augmenting an existing sequential data structure with extra information to support greater functionality is a widely used technique. For example, search trees are augmented to build sequential data structures like order-statistic trees,…
Understanding the boundary between classical simulatability and the power of quantum computation is a fascinating topic. Direct simulation of noisy quantum computation requires solving an open quantum many-body system, which is very costly.…
We consider the problem of duplicate detection in noisy and incomplete data: given a large data set in which each record has multiple entries (attributes), detect which distinct records refer to the same real world entity. This task is…
We initiate the study of tree structures in the context of scenario-based robust optimization. Specifically, we study Binary Search Trees (BSTs) and Huffman coding, two fundamental techniques for efficiently managing and encoding data based…
A new synthesis scheme is proposed to effectively generate a random vector with prescribed joint density that induces a (latent) Gaussian tree structure. The quality of synthesis is measured by total variation distance between the…
There are several data structures which can calculate the prefix sums of an array efficiently, while handling point updates on the array, such as Segment Trees and Binary Indexed Trees (BIT). Both these data structures can handle the these…
Many practical systems can be described by dynamic networks, for which modern technique can measure their output signals, and accumulate extremely rich data. Nevertheless, the network structures producing these data are often deeply hidden…
We introduce a semiparametric approach to neighbor-based classification. We build off the recently proposed Boundary Trees algorithm by Mathy et al.(2015) which enables fast neighbor-based classification, regression and retrieval in large…
Quantum noise is currently limiting efficient quantum information processing and computation. In this work, we consider the tasks of reconstructing and classifying quantum states corrupted by the action of an unknown noisy channel using…
Quantum computing can be employed in computer-aided music composition to control various attributes of the music at different structural levels. This article describes the application of quantum simulation to model compositional decision…
Min-Cut queries are fundamental: Preprocess an undirected edge-weighted graph, to quickly report a minimum-weight cut that separates a query pair of nodes $s,t$. The best data structure known for this problem simply builds a cut-equivalent…
The decision tree recursively partitions the input space into regions and derives axis-aligned decision boundaries from data. Despite its simplicity and interpretability, decision trees lack parameterized representation, which makes it…
We introduce a notion of the quantum query complexity of a certificate structure. This is a formalisation of a well-known observation that many quantum query algorithms only require the knowledge of the disposition of possible certificates…
An algorithm for structured database searching is presented and used to solve the set partition problem. O(n) oracle calls are required in order to obtain a solution, but the probability that this solution is optimal decreases exponentially…
Various modifications of decision trees have been extensively used during the past years due to their high efficiency and interpretability. Tree node splitting based on relevant feature selection is a key step of decision tree learning, at…
Quantum computing promises to improve the information processing power to levels unreachable by classical computation. Quantum walks are heading the development of quantum algorithms for searching information on graphs more efficiently than…