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Related papers: Online Packing to Minimize Area or Perimeter

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The online bisection problem is a natural dynamic variant of the classic optimization problem, where one has to dynamically maintain a partition of $n$ elements into two clusters of cardinality $n/2$. During runtime, an online algorithm is…

Data Structures and Algorithms · Computer Science 2024-03-19 Marcin Bienkowski , Stefan Schmid

We study the online unweighted bipartite matching problem in the random arrival order model, with $n$ offline and $n$ online vertices, in the learning-augmented setting: The algorithm is provided with untrusted predictions of the types…

Machine Learning · Computer Science 2025-12-01 Kunanon Burathep , Thomas Erlebach , William K. Moses

In the online sorting problem, $n$ items are revealed one by one and have to be placed (immediately and irrevocably) into empty cells of a size-$n$ array. The goal is to minimize the sum of absolute differences between items in consecutive…

Data Structures and Algorithms · Computer Science 2024-06-28 Mikkel Abrahamsen , Ioana O. Bercea , Lorenzo Beretta , Jonas Klausen , László Kozma

We initiate a study of the streaming complexity of constraint satisfaction problems (CSPs) when the constraints arrive in a random order. We show that there exists a CSP, namely $\textsf{Max-DICUT}$, for which random ordering makes a…

Data Structures and Algorithms · Computer Science 2023-04-14 Raghuvansh R. Saxena , Noah Singer , Madhu Sudan , Santhoshini Velusamy

One of the main strengths of online algorithms is their ability to adapt to arbitrary data sequences. This is especially important in nonparametric settings, where performance is measured against rich classes of comparator functions that…

Machine Learning · Computer Science 2020-11-03 Ilja Kuzborskij , Nicolò Cesa-Bianchi

In the online metric traveling salesperson problem, $n$ points of a metric space arrive one by one and have to be placed (immediately and irrevocably) into empty cells of a size-$n$ array. The goal is to minimize the sum of distances…

Data Structures and Algorithms · Computer Science 2025-07-08 Christian Bertram

The following online bin packing problem is considered: Items with integer sizes are given and variable sized bins arrive online. A bin must be used if there is still an item remaining which fits in it when the bin arrives. The goal is to…

Data Structures and Algorithms · Computer Science 2018-06-05 Joan Boyar , Faith Ellen

The hitting set problem is one of the fundamental problems in combinatorial optimization and is well-studied in offline setup. We consider the online hitting set problem, where only the set of points is known in advance, and objects are…

Computational Geometry · Computer Science 2024-10-02 Minati De , Ratnadip Mandal , Satyam Singh

Cycle packing is a fundamental problem in optimization, graph theory, and algorithms. Motivated by recent advancements in finding vertex-disjoint paths between a specified set of vertices that either minimize the total length of the paths…

Data Structures and Algorithms · Computer Science 2024-10-28 Matthias Bentert , Fedor V. Fomin , Petr A. Golovach , Tuukka Korhonen , William Lochet , Fahad Panolan , M. S. Ramanujan , Saket Saurabh , Kirill Simonov

The set of 2-dimensional packing problems builds an important class of optimization problems and Strip Packing together with 2-dimensional Bin Packing and 2-dimensional Knapsack is one of the most famous of these problems. Given a set of…

Discrete Mathematics · Computer Science 2019-02-07 Klaus Jansen , Malin Rau

In evaluating an algorithm, worst-case analysis can be overly pessimistic. Average-case analysis can be overly optimistic. An intermediate approach is to show that an algorithm does well on a broad class of input distributions. Koutsoupias…

Data Structures and Algorithms · Computer Science 2015-06-02 Neal E. Young

Within the context of stochastic probing with commitment, we consider the online stochastic matching problem; that is, the one sided online bipartite matching problem where edges adjacent to an online node must be probed to determine if…

Data Structures and Algorithms · Computer Science 2021-01-07 Allan Borodin , Calum MacRury , Akash Rakheja

We study the strip packing problem, a classical packing problem which generalizes both bin packing and makespan minimization. Here we are given a set of axis-parallel rectangles in the two-dimensional plane and the goal is to pack them in a…

Data Structures and Algorithms · Computer Science 2018-01-24 Waldo Gálvez , Fabrizio Grandoni , Salvatore Ingala , Arindam Khan

Orthogonality constraints naturally appear in many machine learning problems, from principal component analysis to robust neural network training. They are usually solved using Riemannian optimization algorithms, which minimize the…

Machine Learning · Statistics 2025-08-08 Pierre Ablin , Simon Vary , Bin Gao , P. -A. Absil

Low-distortional metric embeddings are a crucial component in the modern algorithmic toolkit. In an online metric embedding, points arrive sequentially and the goal is to embed them into a simple space irrevocably, while minimizing the…

Data Structures and Algorithms · Computer Science 2024-11-05 Sujoy Bhore , Arnold Filtser , Csaba D. Tóth

We investigate the problem of computing a minimal-volume container for the non-overlapping packing of a given set of three-dimensional convex objects. Already the simplest versions of the problem are NP-hard so that we cannot expect to find…

Computational Geometry · Computer Science 2016-01-19 Helmut Alt , Nadja Scharf

We introduce a model of online algorithms subject to strict constraints on data retention. An online learning algorithm encounters a stream of data points, one per round, generated by some stationary process. Crucially, each data point can…

Machine Learning · Computer Science 2024-04-18 Nicole Immorlica , Brendan Lucier , Markus Mobius , James Siderius

We consider the classical online scheduling problem P||C_{max} in which jobs are released over list and provide a nearly optimal online algorithm. More precisely, an online algorithm whose competitive ratio is at most (1+\epsilon) times…

Data Structures and Algorithms · Computer Science 2013-02-19 Lin Chen , Deshi Ye , Guochuan Zhang

We consider Online Facility Location in the framework of learning-augmented online algorithms. In Online Facility Location (OFL), demands arrive one-by-one in a metric space and must be (irrevocably) assigned to an open facility upon…

Data Structures and Algorithms · Computer Science 2024-08-20 Dimitris Fotakis , Evangelia Gergatsouli , Themis Gouleakis , Nikolas Patris , Thanos Tolias

Let $P$ be a set of $n$ points in the plane. We show how to find, for a given integer $k>0$, the smallest-area axis-parallel rectangle that covers $k$ points of $P$ in $O(nk^2 \log n+ n\log^2 n)$ time. We also consider the problem of, given…

Computational Geometry · Computer Science 2019-07-12 Mark de Berg , Sergio Cabello , Otfried Cheong , David Eppstein , Christian Knauer