Related papers: Efficiency of Self-Adjusting Heaps
The All-Pairs Shortest Paths (APSP) problem is one of the fundamental problems in theoretical computer science. It asks to compute the distance matrix of a given $n$-vertex graph. We revisit the classical problem of maintaining the distance…
Efficient optimal prefix coding has long been accomplished via the Huffman algorithm. However, there is still room for improvement and exploration regarding variants of the Huffman problem. Length-limited Huffman coding, useful for many…
We present the first potential function for pairing heaps with linear range. This implies that the runtime of a short sequence of operations is faster than previously known. It is also simpler than the only other potential function known to…
A fundamental problem in shape matching and geometric similarity is computing the maximum area overlap between two polygons under translation. For general simple polygons, the best-known algorithm runs in $O((nm)^2 \log(nm))$ time [Mount,…
A maximal matching can be maintained in fully dynamic (supporting both addition and deletion of edges) $n$-vertex graphs using a trivial deterministic algorithm with a worst-case update time of O(n). No deterministic algorithm that…
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.,…
In the problem of adaptive compressed sensing, one wants to estimate an approximately $k$-sparse vector $x\in\mathbb{R}^n$ from $m$ linear measurements $A_1 x, A_2 x,\ldots, A_m x$, where $A_i$ can be chosen based on the outcomes $A_1…
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…
We study the distinct elements and $\ell_p$-heavy hitters problems in the sliding window model, where only the most recent $n$ elements in the data stream form the underlying set. We first introduce the composable histogram, a simple twist…
We study the selection problem, namely that of computing the $i$th order statistic of $n$ given elements. Here we offer a data structure called \emph{selectable sloppy heap} handling a dynamic version in which upon request: (i)~a new…
This work tackles two critical challenges related to the development of metaheuristics for Multi-Objective Optimization Problems (MOOPs): the exponential growth of non-dominated solutions and the tendency of metaheuristics to…
The abelian pattern matching problem consists in finding all substrings of a text which are permutations of a given pattern. This problem finds application in many areas and can be solved in linear time by a naive sliding window approach.…
The simplex method for linear programming is known to be highly efficient in practice, and understanding its performance from a theoretical perspective is an active research topic. The framework of smoothed analysis, first introduced by…
We consider the file maintenance problem (also called the online labeling problem) in which n integer items from the set {1,...,r} are to be stored in an array of size m >= n. The items are presented sequentially in an arbitrary order, and…
In this paper, we investigate optimization problems with nonnegative and orthogonal constraints, where any feasible matrix of size $n \times p$ exhibits a sparsity pattern such that each row accommodates at most one nonzero entry. Our…
We study dynamic $(1+\epsilon)$-approximation algorithms for the all-pairs shortest paths problem in unweighted undirected $n$-node $m$-edge graphs under edge deletions. The fastest algorithm for this problem is a randomized algorithm with…
In this paper, we present a new exact algorithm for counting perfect matchings, which relies on neither inclusion-exclusion principle nor tree-decompositions. For any bipartite graph of $2n$ nodes and $\Delta n$ edges such that $\Delta \geq…
We study the fully dynamic All-Pairs Shortest Paths (APSP) problem in undirected edge-weighted graphs. Given an $n$-vertex graph $G$ with non-negative edge lengths, that undergoes an online sequence of edge insertions and deletions, the…
We describe the first self-indexes able to count and locate pattern occurrences in optimal time within a space bounded by the size of the most popular dictionary compressors. To achieve this result we combine several recent findings,…
The heap is a basic data structure used in a wide variety of applications, including shortest path and minimum spanning tree algorithms. In this paper we explore the design space of comparison-based, amortized-efficient heap…