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The $2$-admissibility of a graph is a promising measure to identify real-world networks which have an algorithmically favourable structure. In contrast to other related measures, like the weak/strong $2$-colouring numbers or the maximum…

Data Structures and Algorithms · Computer Science 2025-05-08 Christine Awofeso , Patrick Greaves , Oded Lachish , Felix Reidl

The Bin Packing Problem is one of the most important optimization problems. In recent years, due to its NP-hard nature, several approximation algorithms have been presented. It is proved that the best algorithm for the Bin Packing Problem…

Data Structures and Algorithms · Computer Science 2015-08-07 Abdolahad Noori Zehmakan

We investigate parameterizing hard combinatorial problems by the size of the solution set compared to all solution candidates. Our main result is a uniform sampling algorithm for satisfying assignments of 2-CNF formulas that runs in…

Discrete Mathematics · Computer Science 2017-08-04 Jean Cardinal , Jerri Nummenpalo , Emo Welzl

We consider the algorithm by Ferson et al. (Reliable computing 11(3), p. 207-233, 2005) designed for solving the NP-hard problem of computing the maximal sample variance over interval data, motivated by robust statistics (in fact, the…

Optimization and Control · Mathematics 2022-07-28 Miroslav Rada , Michal Černý , Ondřej Sokol

The time-optimal $k$-server problem minimizes the time spent serving all requests instead of the distances traveled. We give a lower bound of $2k-1$ on the competitive ratio of any deterministic online algorithm for this problem, which…

Data Structures and Algorithms · Computer Science 2025-03-10 Fabian Frei , Dennis Komm , Moritz Stocker , Philip Whittington

One of the most fundamental problems in Computer Science is the Knapsack problem. Given a set of n items with different weights and values, it asks to pick the most valuable subset whose total weight is below a capacity threshold T. Despite…

Data Structures and Algorithms · Computer Science 2018-07-16 Kyriakos Axiotis , Christos Tzamos

The $k$-cardinality assignment problem asks for finding a maximal (minimal) weight of a matching of cardinality $k$ in a weighted bipartite graph $K_{n,n}$, $k \leq n$. The algorithm of Gassner and Klinz from 2010 for the parametric…

Optimization and Control · Mathematics 2021-04-12 Amnon Rosenmann

The All-Pairs Max-Flow problem has gained significant popularity in the last two decades, and many results are known regarding its fine-grained complexity. Despite this, wide gaps remain in our understanding of the time complexity for…

Data Structures and Algorithms · Computer Science 2024-11-12 Ohad Trabelsi

In the EDGE CLIQUE COVER (ECC) problem, given a graph G and an integer k, we ask whether the edges of G can be covered with k complete subgraphs of G or, equivalently, whether G admits an intersection model on k-element universe. Gramm et…

Data Structures and Algorithms · Computer Science 2012-09-27 Marek Cygan , Marcin Pilipczuk , Michał Pilipczuk

Very recently a new algorithm to the nonnegative single-source shortest path problem on road networks has been discovered. It is very cache-efficient, but only on static road networks. We show how to augment it to the time-dependent…

Data Structures and Algorithms · Computer Science 2010-10-06 Robert Geisberger

We show that approximating the trace norm contraction coefficient of a quantum channel within a constant factor is NP-hard. Equivalently, this shows that determining the optimal success probability for encoding a bit in a quantum system…

Quantum Physics · Physics 2025-09-23 Idris Delsol , Omar Fawzi , Jan Kochanowski , Akshay Ramachandran

We address the problem of coding for classical broadcast channels, which entails maximizing the success probability that can be achieved by sending a fixed number of messages over a broadcast channel. For point-to-point channels, Barman and…

Information Theory · Computer Science 2024-12-10 Omar Fawzi , Paul Fermé

The capacity of a channel can usually be characterized as a maximization of certain entropic quantities. From a practical point of view it is of primary interest to not only compute the capacity value, but also to find the corresponding…

Information Theory · Computer Science 2023-05-25 Holger Boche , Rafael F. Schaefer , H. Vincent Poor

Decentralized optimization with time-varying networks is an emerging paradigm in machine learning. It saves remarkable communication overhead in large-scale deep training and is more robust in wireless scenarios especially when nodes are…

Machine Learning · Computer Science 2022-11-02 Xinmeng Huang , Kun Yuan

The Path Contraction and Cycle Contraction problems take as input an undirected graph $G$ with $n$ vertices, $m$ edges and an integer $k$ and determine whether one can obtain a path or a cycle, respectively, by performing at most $k$ edge…

Data Structures and Algorithms · Computer Science 2024-03-12 R. Krithika , V. K. Kutty Malu , Prafullkumar Tale

In the $k$-dispersion problem, we need to select $k$ nodes of a given graph so as to maximize the minimum distance between any two chosen nodes. This can be seen as a generalization of the independent set problem, where the goal is to…

Data Structures and Algorithms · Computer Science 2017-06-29 Paweł Gawrychowski , Nadav Krasnopolsky , Shay Mozes , Oren Weimann

Knapsack is one of the most fundamental problems in theoretical computer science. In the $(1 - \epsilon)$-approximation setting, although there is a fine-grained lower bound of $(n + 1 / \epsilon) ^ {2 - o(1)}$ based on the $(\min,…

Data Structures and Algorithms · Computer Science 2025-08-12 Xiao Mao

The field of exact exponential time algorithms for NP-hard problems has thrived over the last decade. While exhaustive search remains asymptotically the fastest known algorithm for some basic problems, difficult and non-trivial exponential…

Data Structures and Algorithms · Computer Science 2018-04-24 Marek Cygan , Holger Dell , Daniel Lokshtanov , Daniel Marx , Jesper Nederlof , Yoshio Okamoto , Ramamohan Paturi , Saket Saurabh , Magnus Wahlstrom

Conditional lower bounds for dynamic graph problems has received a great deal of attention in recent years. While many results are now known for the fully-dynamic case and such bounds often imply worst-case bounds for the partially dynamic…

Data Structures and Algorithms · Computer Science 2016-05-04 Søren Dahlgaard

A fundamental problem in shape matching and geometric similarity is computing the maximum area overlap between two polygons under translation. For general simple polygons, the best-known algorithm runs in $O((nm)^2 \log(nm))$ time [Mount,…

Computational Geometry · Computer Science 2025-11-07 Mikkel Abrahamsen , Sujoy Bhore , Maike Buchin , Jacobus Conradi , Ce Jin , André Nusser , Carolin Rehs