Related papers: Mergeable Dictionaries
We introduce a new notion of a relational word as a finite totally ordered set of positions endowed with three binary relations that describe which positions are labeled by equal data, by unequal data and those having an undefined relation…
A dynamic dictionary is a data structure that maintains sets of cardinality at most $n$ from a given universe and supports insertions, deletions, and membership queries. A filter approximates membership queries with a one-sided error that…
A tree-packing is a collection of spanning trees of a graph. It has been a useful tool for computing the minimum cut in static, dynamic, and distributed settings. In particular, [Thorup, Comb. 2007] used them to obtain his dynamic min-cut…
In this paper we consider the following modification of the iterative search problem. We are given a tree $T$, so that a dynamic catalog $C(v)$ is associated with every tree node $v$. For any $x$ and for any node-to-root path $\pi$ in $T$,…
We give the first non-trivial fully dynamic probabilistic tree embedding algorithm for weighted graphs undergoing edge insertions and deletions. We obtain a trade-off between amortized update time and expected stretch against an oblivious…
We present a general transformation for combining a constant number of binary search tree data structures (BSTs) into a single BST whose running time is within a constant factor of the minimum of any "well-behaved" bound on the running time…
A data structure for finite bounded acyclic categories has been built, which is useful to encode and manipulate abstract orientable incidence structure. It can be represented as a directed acyclic multigraph with weighted edges, where the…
The lock-free, ordered, linked list is an important, standard example of a concurrent data structure. An obvious, practical drawback of textbook implementations is that failed compare-and-swap (CAS) operations lead to retraversal of the…
Dynamic or temporal networks enable representation of time-varying edges between nodes. Conventional adjacency-based data structures used for storing networks such as adjacency lists were designed without incorporating time and can thus…
We consider the state complexity of basic operations on tree languages recognized by deterministic unranked tree automata. For the operations of union and intersection the upper and lower bounds of both weakly and strongly deterministic…
We give new deterministic bounds for fully-dynamic graph connectivity. Our data structure supports updates (edge insertions/deletions) in $O(\log^2n/\log\log n)$ amortized time and connectivity queries in $O(\log n/\log\log n)$ worst-case…
The associative operad is a certain algebraic structure on the sequence of group algebras of the symmetric groups. The weak order is a partial order on the symmetric group. There is a natural linear basis of each symmetric group algebra,…
Succinct data structures give space-efficient representations of large amounts of data without sacrificing performance. They rely one cleverly designed data representations and algorithms. We present here the formalization in Coq/SSReflect…
B\"uchi automaton of records (BAR) has been proposed as a basic operational semantics for Reo coordination language. It is an extension of B\"uchi automaton by using a set of records as its alphabet or transition labels. Records are used to…
Skip graphs are a novel distributed data structure, based on skip lists, that provide the full functionality of a balanced tree in a distributed system where resources are stored in separate nodes that may fail at any time. They are…
Previous work on Dynamic Complexity has established that there exist dynamic constant-time parallel algorithms for regular tree languages and context-free languages under label or symbol changes. However, these algorithms were not developed…
This note presents a method of interpreting the tree adjoining languages as the natural third step in a hierarchy that starts with the regular and the context-free languages. The central notion in this account is that of a higher-order…
We introduce a new data structure for answering connectivity queries in undirected graphs subject to batched vertex failures. Precisely, given any graph G and integer k, we can in fixed-parameter time construct a data structure that can…
The dictionary matching problem is to locate occurrences of any pattern among a set of patterns in a given text. Massive data sets abound and at the same time, there are many settings in which working space is extremely limited. We…
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…