Related papers: Red-Black Trees with Constant Update Time
Frequent tree mining asks us to enumerate tree patterns that occur frequently in a database of rooted trees. This problem is motivated by tree-structured data in bioinformatics, such as glycans and pseudoknot-free RNA secondary structures.…
The structure of an evolving network contains information about its past. Extracting this information efficiently, however, is, in general, a difficult challenge. We formulate a fast and efficient method to estimate the most likely history…
We give a Las Vegas data structure which maintains a minimum spanning forest in an n-vertex edge-weighted dynamic graph undergoing updates consisting of any mixture of edge insertions and deletions. Each update is supported in O(n^{1/2 -…
In this paper we generalize the definition of "Search Trees" (ST) to enable reference values other than the key of prior inserted nodes. The idea builds on the assumption an $n$-node AVL (or Red-Black) requires to assure $O(\log_2n)$…
A red-black (RB) tree is a data structure with red and black nodes coloration. The red and black color of nodes make up the principal component for balancing a RB tree. A balanced tree has an equal number of black nodes on any simple path.…
Depth first search (DFS) tree is a fundamental data structure for solving various problems in graphs. It is well known that it takes $O(m+n)$ time to build a DFS tree for a given undirected graph $G=(V,E)$ on $n$ vertices and $m$ edges. We…
We present a Las Vegas algorithm for dynamically maintaining a minimum spanning forest of an $n$-node graph undergoing edge insertions and deletions. Our algorithm guarantees an $O(n^{o(1)})$ worst-case update time with high probability.…
Traditional orthogonal range problems allow queries over a static set of points, each with some value. Dynamic variants allow points to be added or removed, one at a time. To support more powerful updates, we introduce the Grid Range class…
Algorithms for learning decision trees often include heuristic local-search operations such as (1) adjusting the threshold of a cut or (2) also exchanging the feature of that cut. We study minimizing the number of classification errors by…
An anytime decoding algorithm for tree codes using Monte-Carlo tree search is proposed. The meaning of anytime decoding here is twofold: 1) the decoding algorithm is an anytime algorithm, whose decoding performance improves as more…
A dynamic forest data structure maintains a forest (and associated data like edge weights) under edge insertions and deletions. Dynamic forests are widely used to solve online and offline graph problems. Well-known examples of dynamic…
The problem of edge coloring has been extensively studied over the years. Recently, this problem has received significant attention in the dynamic setting, where we are given a dynamic graph evolving via a sequence of edge insertions and…
Spanning trees of low average stretch on the non-tree edges, as introduced by Alon et al. [SICOMP 1995], are a natural graph-theoretic object. In recent years, they have found significant applications in solvers for symmetric diagonally…
In a variety of applications, we need to keep track of the development of a data set over time. For maintaining and querying this multi version data I/O-efficiently, external memory data structures are required. In this paper, we present a…
Consensus maximization is widely used for robust fitting in computer vision. However, solving it exactly, i.e., finding the globally optimal solution, is intractable. A* tree search, which has been shown to be fixed-parameter tractable, is…
We present a decremental data structure for maintaining the SPQR-tree of a planar graph subject to edge contractions and deletions. The update time, amortized over $\Omega(n)$ operations, is $O(\log^2 n)$. Via SPQR-trees, we give a…
It is widely assumed that $O(m+\lg \sigma)$ is the best one can do for finding a pattern of length $m$ in a compacted trie storing strings over an alphabet of size $\sigma$, if one insists on linear-size data structures and deterministic…
We give improved algorithms for maintaining edge-orientations of a fully-dynamic graph, such that the out-degree of each vertex is bounded. On one hand, we show how to orient the edges such that the out-degree of each vertex is proportional…
Dynamic regression trees are an attractive option for automatic regression and classification with complicated response surfaces in on-line application settings. We create a sequential tree model whose state changes in time with the…
Updating and querying on a range is a classical algorithmic problem with a multitude of applications. The Segment Tree data structure is particularly notable in handling the range query and update operations. A Segment Tree divides the…