Related papers: Optimization with pattern-avoiding input
A new pattern search method for bound constrained optimization is introduced. The proposed algorithm employs the coordinate directions, in a suitable way, with a nonmonotone line search for accepting the new iterate, without using…
We consider the problem of minimizing the number of matrix-vector queries needed for accurate trace estimation in the dynamic setting where our underlying matrix is changing slowly, such as during an optimization process. Specifically, for…
We study multi-finger binary search trees (BSTs), a far-reaching extension of the classical BST model, with connections to the well-studied $k$-server problem. Finger search is a popular technique for speeding up BST operations when a query…
The general problem of robust optimization is this: one of several possible scenarios will appear tomorrow, but things are more expensive tomorrow than they are today. What should you anticipatorily buy today, so that the worst-case cost…
We consider a simple optimal probabilistic problem solving strategy that searches through potential solution candidates in a specific order. We are interested in what impact has interchanging the order of two solution candidates with…
Decision tree algorithms have been among the most popular algorithms for interpretable (transparent) machine learning since the early 1980's. The problem that has plagued decision tree algorithms since their inception is their lack of…
We consider a non-stationary variant of a sequential stochastic optimization problem, in which the underlying cost functions may change along the horizon. We propose a measure, termed variation budget, that controls the extent of said…
Given a pattern $P$ and a text $T$, both strings over a binary alphabet, the binary jumbled string matching problem consists in telling whether any permutation of $P$ occurs in $T$. The indexed version of this problem, i.e., preprocessing a…
The paper presents the first \emph{concurrency-optimal} implementation of a binary search tree (BST). The implementation, based on a standard sequential implementation of an internal tree, ensures that every \emph{schedule} is accepted,…
Decision Tree (DT) Learning is a fundamental problem in Interpretable Machine Learning, yet it poses a formidable optimisation challenge. Practical algorithms have recently emerged, primarily leveraging Dynamic Programming and Branch &…
We introduce a new boundedness condition for affine permutations, motivated by the fruitful concept of periodic boundary conditions in statistical physics. We study pattern avoidance in bounded affine permutations. In particular, we show…
This paper presents a detailed comparison of a recently proposed algorithm for optimizing decision trees, tree alternating optimization (TAO), with other popular, established algorithms. We compare their performance on a number of…
We initiate a systematic study of utilizing predictions to improve over approximation guarantees of classic algorithms, without increasing the running time. We propose a systematic method for a wide class of optimization problems that ask…
In a recent paper, Bona and Smith define the notion of \textit{strong avoidance}, in which a permutation and its square both avoid a given pattern. In this paper, we generalize this idea to what we call \textit{chain avoidance}. We say that…
In this paper, we investigate optimization problems with nonnegative and orthogonal constraints, where any feasible matrix of size $n \times p$ exhibits a sparsity pattern such that each row accommodates at most one nonzero entry. Our…
Subset selection with cost constraints aims to select a subset from a ground set to maximize a monotone objective function without exceeding a given budget, which has various applications such as influence maximization and maximum coverage.…
In the online sorting problem, we have an array $A$ of $n$ cells, and receive a stream of $n$ items $x_1,\dots,x_n\in [0,1]$. When an item arrives, we need to immediately and irrevocably place it into an empty cell. The goal is to minimize…
We consider the enumeration of ordered set partitions avoiding a permutation pattern, as introduced by Godbole, Goyt, Herdan and Pudwell. Let $\op_{n,k}(p)$ be the number of ordered set partitions of $\{1,2,\ldots,n\}$ into $k$ blocks that…
In this paper we extend the geometric binary search tree (BST) model of Demaine, Harmon, Iacono, Kane, and Patrascu (DHIKP) to accommodate for insertions and deletions. Within this extended model, we study the online Greedy BST algorithm…
Recombining trinomial trees are a workhorse for modeling discrete-event systems in option pricing, logistics, and feedback control. Because each node stores a state-dependent quantity, a depth-$D$ tree naively yields $\mathcal{O}(3^{D})$…