Related papers: Log-Lists and Their Applications to Sorting by Tra…

The degree distribution of an ordered tree $T$ with $n$ nodes is $\vec{n} = (n_0,\ldots,n_{n-1})$, where $n_i$ is the number of nodes in $T$ with $i$ children. Let $\mathcal{N}(\vec{n})$ be the number of trees with degree distribution…

We present the first in-place algorithm for sorting an array of size n that performs, in the worst case, at most O(n log n) element comparisons and O(n) element transports. This solves a long-standing open problem, stated explicitly, e.g.,…

Given an undirected, weighted graph, the minimum spanning tree (MST) is a tree that connects all of the vertices of the graph with minimum sum of edge weights. In real world applications, network designers often seek to quickly find a…

A central task in string processing is text indexing, where the goal is to preprocess a text (a string of length $n$) into an efficient index (a data structure) supporting queries about the text. Cole, Gottlieb, and Lewenstein (STOC 2004)…

We give an $O(n \log \log n)$ time algorithm for computing the minimum cut (or equivalently, the shortest cycle) of a weighted directed planar graph. This improves the previous fastest $O(n\log^3 n)$ solution. Interestingly, while in…

We consider the problem of maintaining a collection of strings while efficiently supporting splits and concatenations on them, as well as comparing two substrings, and computing the longest common prefix between two suffixes. This problem…

Self-adjusting data structures are a classic approach to adapting the complexity of operations to the data access distribution. While several self-adjusting variants are known for both binary search trees and B-Trees, existing constructions…

In this paper we present novel algorithmic techniques with a O(H(N)+N/H(N)) time complexity for performing several types of queries and updates on general rooted trees, binary search trees and lists of size N. For rooted trees we introduce…

We present time-efficient distributed algorithms for decomposing graphs with large edge or vertex connectivity into multiple spanning or dominating trees, respectively. As their primary applications, these decompositions allow us to achieve…

Edit distance between trees is a natural generalization of the classical edit distance between strings, in which the allowed elementary operations are contraction, uncontraction and relabeling of an edge. Demaine et al. [ACM Trans. on…

In this paper we propose a dynamic data structure that supports efficient algorithms for updating and querying singly connected Bayesian networks (causal trees and polytrees). In the conventional algorithms, new evidence in absorbed in time…

Search trees on trees (STTs) are a far-reaching generalization of binary search trees (BSTs), allowing the efficient exploration of tree-structured domains. (BSTs are the special case in which the underlying domain is a path.) Trees on…

This paper contains a classification of countable lower 1-transitive linear orders. The notion of lower 1-transitivity generalises that of 1-transitivity for linear orders, and is essential for the structure theory of 1-transitive trees.…

The design and implementation of efficient concurrent data structures have seen significant attention. However, most of this work has focused on concurrent data structures providing good \emph{worst-case} guarantees. In real workloads,…

The tree inclusion problem is, given two node-labeled trees $P$ and $T$ (the ``pattern tree'' and the ``target tree''), to locate every minimal subtree in $T$ (if any) that can be obtained by applying a sequence of node insertion operations…

Triangle listing is an important topic significant in many practical applications. Efficient algorithms exist for the task of triangle listing. Recent algorithms leverage an orientation framework, which can be thought of as mapping an…

A seed in a word is a relaxed version of a period in which the occurrences of the repeating subword may overlap. We show a linear-time algorithm computing a linear-size representation of all the seeds of a word (the number of seeds might be…

Linear tree constraints were introduced by Hofmann and Rodriguez in the context of amortized resource analysis for object oriented programs. More precisely, they gave a reduction from inference of resource types to constraint solving. Thus,…

In this paper, we introduce a local search algorithm for hierarchical clustering. For the local step, we consider a tree re-arrangement operation, known as the {\em interchange}, which involves swapping two closely positioned sub-trees…

We study the complexity of finding communication trees with the lowest possible completion time for rooted, irregular gather and scatter collective communication operations in fully connected, $k$-ported communication networks under a…