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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…
We seek decision rules for prediction-time cost reduction, where complete data is available for training, but during prediction-time, each feature can only be acquired for an additional cost. We propose a novel random forest algorithm to…
In this work we study the interleaving distance between merge trees from a combinatorial point of view. We use a particular type of matching between trees to obtain a novel formulation of the distance. With such formulation, we tackle the…
In this article, we give a precise mathematical meaning to `linear? time' that matches experimental behaviour of the algorithm. The sorting algorithm is not our own, it is a variant of radix sort with counting sort as a subroutine. The true…
Suffix trees are key and efficient data structure for solving string problems. A suffix tree is a compressed trie containing all the suffixes of a given text of length $n$ with a linear construction cost. In this work, we introduce an…
The use of machine learning algorithms in finance, medicine, and criminal justice can deeply impact human lives. As a consequence, research into interpretable machine learning has rapidly grown in an attempt to better control and fix…
For general connections, the problem of finding network codes and optimizing resources for those codes is intrinsically difficult and little is known about its complexity. Most of the existing solutions rely on very restricted classes of…
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…
Binary search trees (BSTs) are one of the most basic and widely used data structures. The best static tree for serving a sequence of queries (searches) can be computed by dynamic programming. In contrast, when the BSTs are allowed to be…
We analyze a tree search problem with an underlying Markov decision process, in which the goal is to identify the best action at the root that achieves the highest cumulative reward. We present a new tree policy that optimally allocates a…
Classification and Regression Trees (CARTs) are off-the-shelf techniques in modern Statistics and Machine Learning. CARTs are traditionally built by means of a greedy procedure, sequentially deciding the splitting predictor variable(s) and…
Research in reinforcement learning has produced algorithms for optimal decision making under uncertainty that fall within two main types. The first employs a Bayesian framework, where optimality improves with increased computational time.…
A generic construction of linear codes over finite fields has recently received a lot of attention, and many one-weight, two-weight and three-weight codes with good error correcting capability have been produced with this generic approach.…
Assuming Zipf's Law to be accurate, we show that existing techniques for partially optimizing binary trees produce results that are approximately 10% worse than true optimal. We present a new approximate optimization technique that runs in…
We study a generalized binary search problem on the line and general trees. On the line (e.g., a sorted array), binary search finds a target node in $O(\log n)$ queries in the worst case, where $n$ is the number of nodes. In situations with…
In this paper, we employ group rings and automorphism groups of binary linear codes to construct new record-breaking binary linear codes. We consider the semidirect product of abelian groups and cyclic groups and use these groups to…
A large family of linear codes with flexible parameters from almost bent functions and perfect nonlinear functions are constructed and their parameters are determined. Some constructed linear codes and their related codes are optimal in the…
We investigate at decision trees that incorporate both traditional queries based on one attribute and queries based on hypotheses about the values of all attributes. Such decision trees are similar to ones studied in exact learning, where…
Index codes reduce the number of bits broadcast by a wireless transmitter to a number of receivers with different demands and with side information. It is known that the problem of finding optimal linear index codes is NP-hard. We…
There is a growing body of work on sorting and selection in models other than the unit-cost comparison model. This work is the first treatment of a natural stochastic variant of the problem where the cost of comparing two elements is a…