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Predictive models that generalize well under distributional shift are often desirable and sometimes crucial to building robust and reliable machine learning applications. We focus on distributional shift that arises in causal inference from…

Machine Learning · Statistics 2018-02-27 Fredrik D. Johansson , Nathan Kallus , Uri Shalit , David Sontag

We examine maximum vertex coloring of random geometric graphs, in an arbitrary but fixed dimension, with a constant number of colors. Since this problem is neither scale-invariant nor smooth, the usual methodology to obtain limit laws…

Probability · Mathematics 2016-11-17 Sem Borst , Milan Bradonjić

A new algorithm for exactly sampling from the set of proper colorings of a graph is presented. This is the first such algorithm that has an expected running time that is guaranteed to be linear in the size of a graph with maximum degree \(…

Probability · Mathematics 2026-01-01 Kritika Bhandari , Mark Huber

Irregular computations on unstructured data are an important class of problems for parallel programming. Graph coloring is often an important preprocessing step, e.g. as a way to perform dependency analysis for safe parallel execution. The…

Distributed, Parallel, and Cluster Computing · Computer Science 2015-05-19 Georgios Rokos , Gerard Gorman , Paul H J Kelly

Decompositional parameters such as treewidth are commonly used to obtain fixed-parameter algorithms for NP-hard graph problems. For problems that are W[1]-hard parameterized by treewidth, a natural alternative would be to use a suitable…

Data Structures and Algorithms · Computer Science 2022-03-01 Cornelius Brand , Esra Ceylan , Christian Hatschka , Robert Ganian , Viktoriia Korchemna

A \emph{mixed interval graph} is an interval graph that has, for every pair of intersecting intervals, either an arc (directed arbitrarily) or an (undirected) edge. We are particularly interested in scenarios where edges and arcs are…

Discrete Mathematics · Computer Science 2024-08-09 Grzegorz Gutowski , Konstanty Junosza-Szaniawski , Felix Klesen , Paweł Rzążewski , Alexander Wolff , Johannes Zink

A classic result of Lenstra [Math.~Oper.~Res.~1983] says that an integer linear program can be solved in fixed-parameter tractable (FPT) time for the parameter being the number of variables. We extend this result by incorporating…

Data Structures and Algorithms · Computer Science 2017-11-22 Robert Bredereck , Piotr Faliszewski , Rolf Niedermeier , Piotr Skowron , Nimrod Talmon

The classic greedy coloring (first-fit) algorithm considers the vertices of an input graph $G$ in a given order and assigns the first available color to each vertex $v$ in $G$. In the {\sc Grundy Coloring} problem, the task is to find an…

Discrete Mathematics · Computer Science 2024-10-29 Akanksha Agrawal , Daniel Lokshtanov , Fahad Panolan , Saket Saurabh , Shaily Verma

We study a variation of the graph colouring problem on random graphs of finite average connectivity. Given the number of colours, we aim to maximise the number of different colours at neighbouring vertices (i.e. one edge distance) of any…

Statistical Mechanics · Physics 2009-11-11 S. Bounkong , J. van Mourik , D. Saad

Scheduling problems are fundamental in combinatorial optimization. Much work has been done on approximation algorithms for NP-hard cases, but relatively little is known about exact solutions when some part of the input is a fixed parameter.…

Data Structures and Algorithms · Computer Science 2018-01-09 Dušan Knop , Martin Koutecký

We study the \textsc{Labeled Contractibility} problem, where the input consists of two vertex-labeled graphs $G$ and $H$, and the goal is to determine whether $H$ can be obtained from $G$ via a sequence of edge contractions. Lafond and…

Data Structures and Algorithms · Computer Science 2026-02-12 Yashaswini Mathur , Prafullkumar Tale

A graph is \textit{locally irregular} if the neighbors of every vertex $v$ have degrees distinct from the degree of $v$. \textit{locally irregular edge-coloring} of a graph $G$ is an (improper) edge-coloring such that the graph induced on…

Combinatorics · Mathematics 2018-06-29 Borut Lužar , Jakub Przybyło , Roman Soták

We study the kernel complexity of constraint satisfaction problems over a finite domain, parameterized by the number of variables, whose constraint language consists of two relations: the non-equality relation and an additional…

Computational Complexity · Computer Science 2026-04-24 Ishay Haviv

The notions of bounded expansion and nowhere denseness not only offer robust and general definitions of uniform sparseness of graphs, they also describe the tractability boundary for several important algorithmic questions. In this paper we…

Discrete Mathematics · Computer Science 2019-09-25 Wojciech Nadara , Marcin Pilipczuk , Roman Rabinovich , Felix Reidl , Sebastian Siebertz

Kernelization is an important tool in parameterized algorithmics. Given an input instance accompanied by a parameter, the goal is to compute in polynomial time an equivalent instance of the same problem such that the size of the reduced…

Computational Complexity · Computer Science 2018-10-23 Till Fluschnik , George B. Mertzios , André Nichterlein

An edge-coloring of a graph $G$ with colors $1,2,\ldots,t$ is an interval $t$-coloring if all colors are used, and the colors of edges incident to each vertex of $G$ are distinct and form an interval of integers. A graph $G$ is interval…

Discrete Mathematics · Computer Science 2016-04-01 Hrant H. Khachatrian , Petros A. Petrosyan

In a previous version of this document we misinterpreted the runtime of a part of the described algorithm. Indeed, the runtime is not better than the Grover-Algorithm. We therefor withdraw this work. We present a novel algorithmic approach…

Quantum Physics · Physics 2022-03-04 Michael Epping , Tobias Stollenwerk

We investigate the power of randomized algorithms for the maximum cardinality matching (MCM) and the maximum weight matching (MWM) problems in the online preemptive model. In this model, the edges of a graph are revealed one by one and the…

Data Structures and Algorithms · Computer Science 2015-07-03 Ashish Chiplunkar , Sumedh Tirodkar , Sundar Vishwanathan

For complete graphs and n-cubes bounds are found for the possible number of colours in an interval edge colourings.

Discrete Mathematics · Computer Science 2011-11-10 Petros A. Petrosyan

An improper interval (edge) coloring of a graph $G$ is an assignment of colors to the edges of $G$ satisfying the condition that, for every vertex $v \in V(G)$, the set of colors assigned to the edges incident with $v$ forms an integral…

Combinatorics · Mathematics 2024-06-03 MacKenzie Carr , Eun-Kyung Cho , Nicholas Crawford , Vesna Iršič , Leilani Pai , Rebecca Robinson