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We present the first sublinear-in-$n$ round algorithm for sampling an approximately uniform spanning tree of an $n$-vertex graph in the CongestedClique model of distributed computing. In particular, our algorithm requires…

Distributed, Parallel, and Cluster Computing · Computer Science 2025-05-12 Sriram V. Pemmaraju , Sourya Roy , Joshua Z. Sobel

Recently, span-based constituency parsing has achieved competitive accuracies with extremely simple models by using bidirectional RNNs to model "spans". However, the minimal span parser of Stern et al (2017a) which holds the current state…

Computation and Language · Computer Science 2018-05-23 Juneki Hong , Liang Huang

The suffix trees are fundamental data structures for various kinds of string processing. The suffix tree of a text string $T$ of length $n$ has $O(n)$ nodes and edges, and the string label of each edge is encoded by a pair of positions in…

Data Structures and Algorithms · Computer Science 2023-12-06 Diptarama Hendrian , Takuya Takagi , Shunsuke Inenaga , Keisuke Goto , Mitsuru Funakoshi

We study the Multiple Cluster Scheduling problem and the Multiple Strip Packing problem. For both problems, there is no algorithm with approximation ratio better than $2$ unless $P = NP$. In this paper, we present an algorithm with…

Data Structures and Algorithms · Computer Science 2019-02-12 Klaus Jansen , Malin Rau

We present an all-pairs shortest path algorithm whose running time on a complete directed graph on $n$ vertices whose edge weights are chosen independently and uniformly at random from $[0,1]$ is $O(n^2)$, in expectation and with high…

Combinatorics · Mathematics 2011-05-20 Yuval Peres , Dimitry Sotnikov , Benny Sudakov , Uri Zwick

Probabilistic distributions over spanning trees in directed graphs are a fundamental model of dependency structure in natural language processing, syntactic dependency trees. In NLP, dependency trees often have an additional root…

Computation and Language · Computer Science 2022-07-11 Ran Zmigrod , Tim Vieira , Ryan Cotterell

It is shown that every tree of size $n$ over a fixed set of $\sigma$ different ranked symbols can be decomposed (in linear time as well as in logspace) into $O\big(\frac{n}{\log_\sigma n}\big) = O\big(\frac{n \log \sigma}{\log n}\big)$ many…

Data Structures and Algorithms · Computer Science 2015-09-22 Moses Ganardi , Danny Hucke , Artur Jez , Markus Lohrey , Eric Noeth

We consider the NP-hard problem of finding a spanning tree with a maximum number of internal vertices. This problem is a generalization of the famous Hamiltonian Path problem. Our dynamic-programming algorithms for general and…

Data Structures and Algorithms · Computer Science 2009-06-12 Henning Fernau , Serge Gaspers , Daniel Raible

The suffix array is a fundamental data structure for many applications that involve string searching and data compression. Designing time/space-efficient suffix array construction algorithms has attracted significant attention and…

Data Structures and Algorithms · Computer Science 2018-11-12 Zhize Li , Jian Li , Hongwei Huo

An archetypal problem discussed in computer science is the problem of searching for a given number in a given set of numbers. Other than sequential search, the classic solution is to sort the list of numbers and then apply binary search.…

Computational Complexity · Computer Science 2015-03-20 Philon Nguyen

The equidistant subsequence pattern matching problem is considered. Given a pattern string $P$ and a text string $T$, we say that $P$ is an \emph{equidistant subsequence} of $T$ if $P$ is a subsequence of the text such that consecutive…

Data Structures and Algorithms · Computer Science 2020-02-18 Mitsuru Funakoshi , Yuto Nakashima , Shunsuke Inenaga , Hideo Bannai , Masayuki Takeda , Ayumi Shinohara

We investigate the complexity of several fundamental polynomial-time solvable problems on graphs and on matrices, when the given instance has low treewidth; in the case of matrices, we consider the treewidth of the graph formed by non-zero…

Data Structures and Algorithms · Computer Science 2015-11-05 Fedor V. Fomin , Daniel Lokshtanov , Michał Pilipczuk , Saket Saurabh , Marcin Wrochna

We study sublinear time algorithms for estimating the size of maximum matching in graphs. Our main result is a $(\frac{1}{2}+\Omega(1))$-approximation algorithm which can be implemented in $O(n^{1+\epsilon})$ time, where $n$ is the number…

Data Structures and Algorithms · Computer Science 2022-06-28 Soheil Behnezhad , Mohammad Roghani , Aviad Rubinstein , Amin Saberi

We describe new, simple, recursive methods of construction for orientable sequences over an arbitrary finite alphabet, i.e. periodic sequences in which any sub-sequence of n consecutive elements occurs at most once in a period in either…

Combinatorics · Mathematics 2026-03-20 Abbas Alhakim , Chris J. Mitchell , Janusz Szmidt , Peter R. Wild

(I) We revisit the algorithmic problem of finding all triangles in a graph $G=(V,E)$ with $n$ vertices and $m$ edges. According to a result of Chiba and Nishizeki (1985), this task can be achieved by a combinatorial algorithm running in…

Data Structures and Algorithms · Computer Science 2026-02-18 Ke Chen , Adrian Dumitrescu , Andrzej Lingas

We provide linear-time algorithms for geometric graphs with sublinearly many crossings. That is, we provide algorithms running in O(n) time on connected geometric graphs having n vertices and k crossings, where k is smaller than n by an…

Computational Geometry · Computer Science 2010-12-16 David Eppstein , Michael T. Goodrich , Darren Strash

Recently Kubica et al. (Inf. Process. Let., 2013) and Kim et al. (submitted to Theor. Comp. Sci.) introduced order-preserving pattern matching. In this problem we are looking for consecutive substrings of the text that have the same "shape"…

We consider string matching with variable length gaps. Given a string $T$ and a pattern $P$ consisting of strings separated by variable length gaps (arbitrary strings of length in a specified range), the problem is to find all ending…

Data Structures and Algorithms · Computer Science 2011-10-14 Philip Bille , Inge Li Goertz , Hjalte Wedel Vildhøj , David Kofoed Wind

Motivated by computing duplication patterns in sequences, a new fundamental problem called the longest subsequence-repeated subsequence (LSRS) is proposed. Given a sequence $S$ of length $n$, a letter-repeated subsequence is a subsequence…

Data Structures and Algorithms · Computer Science 2023-09-01 Manuel Lafond , Wenfeng Lai , Adiesha Liyanage , Binhai Zhu

In binary jumbled pattern matching we wish to preprocess a binary string $S$ in order to answer queries $(i,j)$ which ask for a substring of $S$ that is of size $i$ and has exactly $j$ 1-bits. The problem naturally generalizes to…

Data Structures and Algorithms · Computer Science 2014-07-01 Danny Hermelin , Gad M. Landau , Yuri Rabinovich , Oren Weimann