Related papers: An O(loglog n)-Competitive Binary Search Tree with…
We present a complete classification of the deterministic distributed time complexity for a family of graph problems: binary labeling problems in trees. These are locally checkable problems that can be encoded with an alphabet of size two…
Important papers have appeared recently on the problem of indexing binary strings for jumbled pattern matching, and further lowering the time bounds in terms of the input size would now be a breakthrough with broad implications. We can…
A classic data structure problem is to preprocess a string T of length $n$ so that, given a query $q$, we can quickly find all substrings of T with Hamming distance at most $k$ from the query string. Variants of this problem have seen…
We significantly improve known time bounds for solving the minimum cut problem on undirected graphs. We use a ``semi-duality'' between minimum cuts and maximum spanning tree packings combined with our previously developed random sampling…
The pairing heap is a simple "self-adjusting" implementation of a heap (priority queue). Inserting an item into a pairing heap or decreasing the key of an item takes O(1) time worst-case, as does melding two heaps. But deleting an item of…
In this paper we present an efficient reachability oracle under single-edge or single-vertex failures for planar directed graphs. Specifically, we show that a planar digraph $G$ can be preprocessed in $O(n\log^2{n}/\log\log{n})$ time,…
We study a document retrieval problem in the new framework where $D$ text documents are organized in a {\em category tree} with a pre-defined number $h$ of categories. This situation occurs e.g. with taxomonic trees in biology or subject…
Polytrees are a subclass of Bayesian networks that seek to capture the conditional dependencies between a set of $n$ variables as a directed forest and are motivated by their more efficient inference and improved interpretability. Since the…
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…
The fully-functional succinct tree representation of Navarro and Sadakane (ACM Transactions on Algorithms, 2014) supports a large number of operations in constant time using $2n+o(n)$ bits. However, the full idea is hard to implement. Only…
Given two rooted, ordered, and labeled trees $P$ and $T$ the tree inclusion problem is to determine if $P$ can be obtained from $T$ by deleting nodes in $T$. This problem has recently been recognized as an important query primitive in XML…
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…
We consider the dictionary problem in external memory and improve the update time of the well-known buffer tree by roughly a logarithmic factor. For any \lambda >= max {lg lg n, log_{M/B} (n/B)}, we can support updates in time O(\lambda /…
Adaptive binary search trees are a fundamental data structure for organizing hierarchical information. Their ability to dynamically adjust to access patterns makes them particularly valuable for building responsive and efficient networked…
Navarro and Sadakane [TALG 2014] gave a dynamic succinct data structure for storing an ordinal tree. The structure supports tree queries in either $O(\log n/\log\log n)$ or $O(\log n)$ time, and insertion or deletion of a single node in…
In the online Steiner forest problem we are given a graph $G$, and a sequence of terminal pairs $(u_i,v_i)$ which arrive in an online fashion. We are asked to maintain a low-cost subgraph in which each $u_i$ is connected to $v_i$ for all…
We consider online algorithms for the $k$-server problem on trees of size $n$. Chrobak and Larmore proposed a $k$-competitive algorithm for this problem that has the optimal competitive ratio. However, the existing implementations have…
Given two point sets $R$ and $B$ in the plane, with cardinalities $m$ and $n$, respectively, and each set stored in a separate R-tree, we present an algorithm to decide whether $R$ and $B$ are linearly separable. Our algorithm exploits the…
We introduce online probabilistic label trees (OPLTs), an algorithm that trains a label tree classifier in a fully online manner without any prior knowledge about the number of training instances, their features and labels. OPLTs are…
I present a parallel algorithm for exact probabilistic inference in Bayesian networks. For polytree networks with n variables, the worst-case time complexity is O(log n) on a CREW PRAM (concurrent-read, exclusive-write parallel…