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A decision tree recursively splits a feature space $\mathbb{R}^{d}$ and then assigns class labels based on the resulting partition. Decision trees have been part of the basic machine-learning toolkit for decades. A large body of work treats…

A matching is a set of edges in a graph with no common endpoint. A matching M is called acyclic if the induced subgraph on the endpoints of the edges in M is acyclic. Given a graph G and an integer k, Acyclic Matching Problem seeks for an…

Computational Complexity · Computer Science 2022-10-05 Sahab Hajebi , Ramin Javadi

We continue and extend previous work on the parameterized complexity analysis of the NP-hard Stable Roommates with Ties and Incomplete Lists problem, thereby strengthening earlier results both on the side of parameterized hardness as well…

Computational Complexity · Computer Science 2021-03-09 Robert Bredereck , Klaus Heeger , Dušan Knop , Rolf Niedermeier

This paper deals with the size of the spanning tree of p randomly chosen nodes in a binary search tree. It is shown via generating functions methods, that for fixed p, the (normalized) spanning tree size converges in law to the Normal…

Probability · Mathematics 2007-05-23 Alois Panholzer , Helmut Prodinger

Computing a minimum-area planar straight-line drawing of a graph is known to be NP-hard for planar graphs, even when restricted to outerplanar graphs. However, the complexity question is open for trees. Only a few hardness results are known…

Computational Geometry · Computer Science 2017-09-01 Therese Biedl , Debajyoti Mondal

Cartesian tree pattern matching consists of finding all the factors of a text that have the same Cartesian tree than a given pattern. There already exist theoretical and practical solutions for the exact case. In this paper, we propose the…

Data Structures and Algorithms · Computer Science 2025-05-15 Bastien Auvray , Julien David , Samah Ghazawi , Richard Groult , Gad M. Landau , Thierry Lecroq

In this paper, we consider the minimum spanning tree problem (for short, MSTP) on an arbitrary set of $n$ points of $d$-dimensional space in $l_1$-norm. For this problem, for each fixed $d\geq 2$, there is a known algorithm of the…

Discrete Mathematics · Computer Science 2024-12-12 K. V. Kaymakov , D. S. Malyshev

We define simple variants of zip trees, called zip-zip trees, which provide several advantages over zip trees, including overcoming a bias that favors smaller keys over larger ones. We analyze zip-zip trees theoretically and empirically,…

Data Structures and Algorithms · Computer Science 2025-02-11 Ofek Gila , Michael T. Goodrich , Robert E. Tarjan

While obtaining optimal algorithms for the most important problems in the LOCAL model has been one of the central goals in the area of distributed algorithms since its infancy, tight complexity bounds are elusive for many problems even when…

Distributed, Parallel, and Cluster Computing · Computer Science 2025-05-06 Sebastian Brandt , Ananth Narayanan

In the context of tree-search stochastic planning algorithms where a generative model is available, we consider on-line planning algorithms building trees in order to recommend an action. We investigate the question of avoiding re-planning…

Machine Learning · Computer Science 2019-02-14 Erwan Lecarpentier , Guillaume Infantes , Charles Lesire , Emmanuel Rachelson

We consider partitions of a point set into two parts, and the lengths of the minimum spanning trees of the original set and of the two parts. If $w(P)$ denotes the length of a minimum spanning tree of $P$, we show that every set $P$ of $n…

Computational Geometry · Computer Science 2024-01-02 Adrian Dumitrescu , János Pach , Géza Tóth

Graph isomorphism, subgraph isomorphism, and maximum common subgraphs are classical well-investigated objects. Their (parameterized) complexity and efficiently tractable cases have been studied. In the present paper, for a given set of…

Data Structures and Algorithms · Computer Science 2024-03-22 Dieter Rautenbach , Florian Werner

{\em Reoptimization} is a setting in which we are given an (near) optimal solution of a problem instance and a local modification that slightly changes the instance. The main goal is that of finding an (near) optimal solution of the…

Data Structures and Algorithms · Computer Science 2018-05-01 Davide Bilò

A tremendous range of design tasks in materials, physics, and biology can be formulated as finding the optimum of an objective function depending on many parameters without knowing its closed-form expression or the derivative. Traditional…

Machine Learning · Computer Science 2024-04-08 Ye Wei , Bo Peng , Ruiwen Xie , Yangtao Chen , Yu Qin , Peng Wen , Stefan Bauer , Po-Yen Tung

Perfect Matching-Cut is the problem of deciding whether a graph has a perfect matching that contains an edge-cut. We show that this problem is NP-complete for planar graphs with maximum degree four, for planar graphs with girth five, for…

Combinatorics · Mathematics 2021-11-01 Valentin Bouquet , Christophe Picouleau

A secure set $S$ in a graph is defined as a set of vertices such that for any $X\subseteq S$ the majority of vertices in the neighborhood of $X$ belongs to $S$. It is known that deciding whether a set $S$ is secure in a graph is…

Computational Complexity · Computer Science 2017-07-11 Bernhard Bliem , Stefan Woltran

Given an $n$-vertex non-negatively real-weighted graph $G$, whose vertices are partitioned into a set of $k$ clusters, a \emph{clustered network design problem} on $G$ consists of solving a given network design optimization problem on $G$,…

Data Structures and Algorithms · Computer Science 2018-02-01 Mattia D'Emidio , Luca Forlizzi , Daniele Frigioni , Stefano Leucci , Guido Proietti

We consider the indirect covering subtree problem (Kim et al., 1996). The input is an edge weighted tree graph along with customers located at the nodes. Each customer is associated with a radius and a penalty. The goal is to locate a…

Data Structures and Algorithms · Computer Science 2010-02-03 Joachim Spoerhase

We present a general technique, based on parametric search with some twist, for solving a variety of optimization problems on a set of semi-algebraic geometric objects of constant complexity. The common feature of these problems is that…

Computational Geometry · Computer Science 2022-07-15 Matthew J. Katz , Micha Sharir

We study learning-augmented binary search trees (BSTs) via Treaps with carefully designed priorities. The result is a simple search tree in which the depth of each item $x$ is determined by its predicted weight $w_x$. Specifically, each…

Data Structures and Algorithms · Computer Science 2025-05-16 Jingbang Chen , Xinyuan Cao , Alicia Stepin , Li Chen