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Given a signed permutation on $n$ elements, we need to sort it with the fewest reversals. This is a fundamental algorithmic problem motivated by applications in comparative genomics, as it allows to accurately model rearrangements in small…

Data Structures and Algorithms · Computer Science 2023-08-31 Bartłomiej Dudek , Paweł Gawrychowski , Tatiana Starikovskaya

We present a new approximation algorithm for the treewidth problem which finds an upper bound on the treewidth and constructs a corresponding tree decomposition as well. Our algorithm is a faster variation of Reed's classical algorithm. For…

Data Structures and Algorithms · Computer Science 2022-06-24 Mahdi Belbasi , Martin Fürer

We give an algorithm that, given an $n$-vertex graph $G$ and an integer $k$, in time $2^{O(k)} n$ either outputs a tree decomposition of $G$ of width at most $2k + 1$ or determines that the treewidth of $G$ is larger than $k$. This is the…

Data Structures and Algorithms · Computer Science 2023-08-24 Tuukka Korhonen

The Permutation Pattern Matching problem, asking whether a pattern permutation $\pi$ is contained in a permutation $\tau$, is known to be NP-complete. In this paper we present two polynomial time algorithms for special cases. The first…

Combinatorics · Mathematics 2023-06-22 Michael H. Albert , Marie-Louise Lackner , Martin Lackner , Vincent Vatter

We present an efficient algorithm for finding all approximate occurrences of a given pattern $p$ of length $m$ in a text $t$ of length $n$ allowing for translocations of equal length adjacent factors and inversions of factors. The algorithm…

Data Structures and Algorithms · Computer Science 2013-05-09 Szymon Grabowski , Simone Faro , Emanuele Giaquinta

A common complaint about adaptive prefix coding is that it is much slower than static prefix coding. Karpinski and Nekrich recently took an important step towards resolving this: they gave an adaptive Shannon coding algorithm that encodes…

Information Theory · Computer Science 2008-12-18 Travis Gagie , Yakov Nekrich

Approximate Pattern Matching is among the most fundamental string-processing tasks. Given a text $T$ of length $n$, a pattern $P$ of length $m$, and a threshold $k$, the task is to identify the fragments of $T$ that are at distance at most…

Data Structures and Algorithms · Computer Science 2024-10-10 Tomasz Kociumaka , Jakob Nogler , Philip Wellnitz

Given a set $Z$ of $n$ positive integers and a target value $t$, the Subset Sum problem asks whether any subset of $Z$ sums to $t$. A textbook pseudopolynomial time algorithm by Bellman from 1957 solves Subset Sum in time $O(nt)$. This has…

Data Structures and Algorithms · Computer Science 2017-01-10 Karl Bringmann

Given $n$ jobs with processing times $p_1,\dotsc,p_n\in\mathbb N$ and $m\le n$ machines with speeds $s_1,\dotsc,s_m\in\mathbb N$ our goal is to allocate the jobs to machines minimizing the makespan. We present an algorithm that solves the…

Data Structures and Algorithms · Computer Science 2025-01-10 Lars Rohwedder

An algorithm is presented for unranking permutations in transposition order: Given a seed s\in N, the algorithm produces a permutation P(s) that differs from the permutation P(s+1) by the transposition of two elements.

Combinatorics · Mathematics 2008-06-10 Konstantinos A. Blekos

An upper dominating set is a minimal dominating set in a graph. In the \textsc{Upper Dominating Set} problem, the goal is to find an upper dominating set of maximum size. We study the complexity of parameterized algorithms for \textsc{Upper…

Data Structures and Algorithms · Computer Science 2021-01-20 Louis Dublois , Michael Lampis , Vangelis Th. Paschos

We give a space-optimal algorithm with update time O(log^2(1/eps)loglog(1/eps)) for (1+eps)-approximating the pth frequency moment, 0 < p < 2, of a length-n vector updated in a data stream. This provides a nearly exponential improvement in…

Data Structures and Algorithms · Computer Science 2010-07-26 Daniel M. Kane , Jelani Nelson , Ely Porat , David P. Woodruff

The Cut & Count technique and the rank-based approach have lead to single-exponential FPT algorithms parameterized by treewidth, that is, running in time $2^{O(tw)}n^{O(1)}$, for Feedback Vertex Set and connected versions of the classical…

Data Structures and Algorithms · Computer Science 2020-07-29 Benjamin Bergougnoux , Édouard Bonnet , Nick Brettell , O-joung Kwon

We show that the edit distance between two run-length encoded strings of compressed lengths $m$ and $n$ respectively, can be computed in $\mathcal{O}(mn\log(mn))$ time. This improves the previous record by a factor of…

Data Structures and Algorithms · Computer Science 2019-05-06 Raphaël Clifford , Paweł Gawrychowski , Tomasz Kociumaka , Daniel P. Martin , Przemysław Uznański

Subset Sum Ratio is the following optimization problem: Given a set of $n$ positive numbers $I$, find disjoint subsets $X,Y \subseteq I$ minimizing the ratio $\max\{\Sigma(X)/\Sigma(Y),\Sigma(Y)/\Sigma(X)\}$, where $\Sigma(Z)$ denotes the…

Data Structures and Algorithms · Computer Science 2023-10-12 Karl Bringmann

In this paper we analyze the expected time complexity of the auction algorithm for the matching problem on random bipartite graphs. We prove that the expected time complexity of the auction algorithm for bipartite matching is…

Data Structures and Algorithms · Computer Science 2017-04-07 Oshri Naparstek , Amir Leshem

We consider the problem of sorting $n$ elements subject to persistent random comparison errors. In this problem, each comparison between two elements can be wrong with some fixed (small) probability $p$, and comparing the same pair of…

Data Structures and Algorithms · Computer Science 2025-08-28 Barbara Geissmann , Stefano Leucci , Chih-Hung Liu , Paolo Penna

We revisit the problem of permuting an array of length $n$ according to a given permutation in place, that is, using only a small number of bits of extra storage. Fich, Munro and Poblete [FOCS 1990, SICOMP 1995] obtained an elegant…

Data Structures and Algorithms · Computer Science 2021-01-12 Bartłomiej Dudek , Paweł Gawrychowski , Karol Pokorski

Bellman's algorithm for Subset Sum is one of the earliest and simplest examples of dynamic programming, dating back to 1957. For a given set of $n$ integers $X$ and a target $t$, it computes the set of subset sums $\mathcal S(X, t)$ (i.e.,…

Data Structures and Algorithms · Computer Science 2024-10-30 Karl Bringmann , Nick Fischer , Vasileios Nakos

Given a multiset $X=\{x_1,..., x_n\}$ of real numbers, the {\it floating-point set summation} problem asks for $S_n=x_1+...+x_n$. Let $E^*_n$ denote the minimum worst-case error over all possible orderings of evaluating $S_n$. We prove that…

Data Structures and Algorithms · Computer Science 2024-09-21 Ming-Yang Kao , Jie Wang