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Avraham et al. [AFK+15] presented an alternative approach to parametric search, called \emph{bifurcation}, that performs faster under certain circumstances. Intuitively, when the underlying decider execution can be rolled back cheaply and…
We initiate a study of a query-driven approach to designing partition trees for range-searching problems. Our model assumes that a data structure is to be built for an unknown query distribution that we can access through a sampling oracle,…
We give an improved connectivity oracle under vertex failures. After a set of $k$ vertices fails, our oracle performs an $O(k^{6})$-time update independent of the graph size $n$, and then answers pairwise connectivity queries in optimal…
Consider a forest that evolves via $link$ operations that make the root of one tree the child of a node in another tree. Intermixed with $link$ operations are $nca$ operations, which return the nearest common ancestor of two given nodes…
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 revisit the vertex-failure connectivity oracle problem. This is one of the most basic graph data structure problems under vertex updates, yet its complexity is still not well-understood. We essentially settle the complexity of this…
Sorting has a natural generalization where the input consists of: (1) a ground set $X$ of size $n$, (2) a partial oracle $O_P$ specifying some fixed partial order $P$ on $X$ and (3) a linear oracle $O_L$ specifying a linear order $L$ that…
We consider online algorithms for the $k$-server problem on trees. Chrobak and Larmore proposed a $k$-competitive algorithm for this problem that has the optimal competitive ratio. However, a naive implementation of their algorithm has…
We suggest a new non-recursive algorithm for constructing a binary search tree given an array of numbers. The algorithm has $O(N)$ time and $O(1)$ memory complexity if the given array of $N$ numbers is sorted. The resulting tree is of…
We describe a framework for maintaining forest algebra representations that are of logarithmic height for unranked trees. Such representations can be computed in O(n) time and updated in O(log(n)) time. The framework is of potential…
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,…
Let $G=(V,E)$ be an undirected unweighted graph on $n$ vertices and $m$ edges. We address the problem of sensitivity oracle for all-pairs mincuts in $G$ defined as follows. Build a compact data structure that, on receiving any pair of…
We study networks obeying \emph{time-dependent} min-cost path metrics, and present novel oracles for them which \emph{provably} achieve two unique features: % (i) \emph{subquadratic} preprocessing time and space, \emph{independent} of the…
A minimum cycle basis of a weighted undirected graph $G$ is a basis of the cycle space of $G$ such that the total weight of the cycles in this basis is minimized. If $G$ is a planar graph with non-negative edge weights, such a basis can be…
Given a weighted, ordered query set $Q$ and a partition of $Q$ into classes, we study the problem of computing a minimum-cost decision tree that, given any query $q$ in $Q$, uses equality tests and less-than comparisons to determine the…
This work considers a number of optimization problems and reductive relations between them. The two main problems we are interested in are the \emph{Optimal Decision Tree} and \emph{Set Cover}. We study these two fundamental tasks under…
Identifying the top-$k$ items is fundamental but often prohibitive when exact valuations are expensive. We study a two-oracle setting with a fast, noisy weak oracle and a scarce, high-fidelity strong oracle (e.g., human expert verification…
Motivated by an application in computational topology, we consider a novel variant of the problem of efficiently maintaining dynamic rooted trees. This variant requires merging two paths in a single operation. In contrast to the standard…
Given a graph of which the n vertices form a regular two-dimensional grid, and in which each (possibly weighted and/or directed) edge connects a vertex to one of its eight neighbours, the following can be done in O(scan(n)) I/Os, provided M…
A (1 + eps)-approximate distance oracle for a graph is a data structure that supports approximate point-to-point shortest-path-distance queries. The most relevant measures for a distance-oracle construction are: space, query time, and…