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Dynamic programming on various graph decompositions is one of the most fundamental techniques used in parameterized complexity. Unfortunately, even if we consider concepts as simple as path or tree decompositions, such dynamic programming…

We give an algorithm for finding the arboricity of a weighted, undirected graph, defined as the minimum number of spanning forests that cover all edges of the graph, in $\sqrt{n} m^{1+o(1)}$ time. This improves on the previous best bound of…

Data Structures and Algorithms · Computer Science 2025-07-22 Ruoxu Cen , Henry Fleischmann , George Z. Li , Jason Li , Debmalya Panigrahi

We present a new universal source code for distributions of unlabeled binary and ordinal trees that achieves optimal compression to within lower order terms for all tree sources covered by existing universal codes. At the same time, it…

Data Structures and Algorithms · Computer Science 2021-09-06 J. Ian Munro , Patrick K. Nicholson , Louisa Seelbach Benkner , Sebastian Wild

We study the problem of minimizing a multivariate polynomial function over the unit hypercube. By representing the polynomial through a hypergraph and exploiting its sparsity structure, we establish a new sufficient condition under which…

Optimization and Control · Mathematics 2026-04-29 Aida Khajavirad

We study the problem of decomposing (clustering) a tree with respect to costs attributed to pairs of nodes, so as to minimize the sum of costs for those pairs of nodes that are in the same component (cluster). For the general case and for…

Discrete Mathematics · Computer Science 2017-08-17 Jan-Hendrik Lange , Bjoern Andres

We consider optimal route planning when the objective function is a general nonlinear and non-monotonic function. Such an objective models user behavior more accurately, for example, when a user is risk-averse, or the utility function needs…

Data Structures and Algorithms · Computer Science 2015-11-24 Ger Yang , Evdokia Nikolova

We show how to construct an overlay network of constant degree and diameter $O(\log n)$ in time $O(\log n)$ starting from an arbitrary weakly connected graph. We assume a synchronous communication network in which nodes can send messages to…

Distributed, Parallel, and Cluster Computing · Computer Science 2021-07-28 Thorsten Götte , Kristian Hinnenthal , Christian Scheideler , Julian Werthmann

Label tree-based algorithms are widely used to tackle multi-class and multi-label problems with a large number of labels. We focus on a particular subclass of these algorithms that use probabilistic classifiers in the tree nodes. Examples…

Treewidth and hypertree width have proven to be highly successful structural parameters in the context of the Constraint Satisfaction Problem (CSP). When either of these parameters is bounded by a constant, then CSP becomes solvable in…

Data Structures and Algorithms · Computer Science 2022-10-14 Andre Schidler , Robert Ganian , Manuel Sorge , Stefan Szeider

Finding an optimal assignment between two sets of objects is a fundamental problem arising in many applications, including the matching of `bag-of-words' representations in natural language processing and computer vision. Solving the…

Machine Learning · Computer Science 2019-09-12 Nils M. Kriege , Pierre-Louis Giscard , Franka Bause , Richard C. Wilson

{\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

We discuss a simple, binary tree-based algorithm for the collective allreduce (reduction-to-all, MPI_Allreduce) operation for parallel systems consisting of $p$ suitably interconnected processors. The algorithm can be doubly pipelined to…

Distributed, Parallel, and Cluster Computing · Computer Science 2022-01-21 Jesper Larsson Träff

We develop a general framework for designing polynomial-time approximation schemes (PTASs) for various vehicle routing problems in trees. In these problems, the goal is to optimally route a fleet of vehicles, originating at a depot, to…

Data Structures and Algorithms · Computer Science 2019-02-27 Amariah Becker , Alice Paul

We give the first data structure for the problem of maintaining a dynamic set of n elements drawn from a partially ordered universe described by a tree. We define the Line-Leaf Tree, a linear-sized data structure that supports the…

Data Structures and Algorithms · Computer Science 2011-05-03 Brent Heeringa , Marius Catalin Iordan , Louis Theran

We consider the problem of learning underlying tree structure from noisy, mixed data obtained from a linear model. To achieve this, we use the expectation maximization algorithm combined with Chow-Liu minimum spanning tree algorithm. This…

Information Theory · Computer Science 2017-10-06 Navid Tafaghodi Khajavi

The range-minimum query (RMQ) problem is a fundamental data structuring task with numerous applications. Despite the fact that succinct solutions with worst-case optimal $2n+o(n)$ bits of space and constant query time are known, it has been…

Data Structures and Algorithms · Computer Science 2019-03-07 J. Ian Munro , Sebastian Wild

We consider the well-studied problem of finding a spanning tree with minimum average distance between vertex pairs (called a MAD tree). This is a classic network design problem which is known to be NP-hard. While approximation algorithms…

Data Structures and Algorithms · Computer Science 2026-04-01 Tom-Lukas Breitkopf , Vincent Froese , Anton Herrmann , André Nichterlein , Camille Richer

Given a graph G, the {\em maximum internal spanning tree problem} (MIST for short) asks for computing a spanning tree T of G such that the number of internal vertices in T is maximized. MIST has possible applications in the design of…

Data Structures and Algorithms · Computer Science 2016-08-02 Zhi-Zhong Chen , Youta Harada , Lusheng Wang

Tree-based machine learning models such as random forests, decision trees, and gradient boosted trees are the most popular non-linear predictive models used in practice today, yet comparatively little attention has been paid to explaining…

Suffix tree (and the closely related suffix array) are fundamental structures capturing all substrings of a given text essentially by storing all its suffixes in the lexicographical order. In some applications, we work with a subset of $b$…

Data Structures and Algorithms · Computer Science 2016-08-03 Paweł Gawrychowski , Tomasz Kociumaka