Related papers: Sorting under Partial Information with Optimal Pre…

We present a new approach for solving (minimum disagreement) correlation clustering that results in sublinear algorithms with highly efficient time and space complexity for this problem. In particular, we obtain the following algorithms for…

TimSort is a well-established sorting algorithm whose running time depends on how sorted the input already is. Recently, Eppstein, Goodrich, Illickan, and To designed algorithms inspired by TimSort for Pareto front, planar convex hull, and…

Since its introduction to computational geometry by Alt and Godau in 1992, the Fr\'echet distance has been a mainstay of algorithmic research on curve similarity computations. The focus of the research has been on comparing polygonal…

We explore the fundamental problem of sorting through the lens of learning-augmented algorithms, where algorithms can leverage possibly erroneous predictions to improve their efficiency. We consider two different settings: In the first…

In edge orientations, the goal is usually to orient (direct) the edges of an undirected $n$-vertex graph $G$ such that all out-degrees are bounded. When the graph $G$ is fully dynamic, i.e., admits edge insertions and deletions, we wish to…

We study faster algorithms for producing the minimum degree ordering used to speed up Gaussian elimination. This ordering is based on viewing the non-zero elements of a symmetric positive definite matrix as edges of an undirected graph, and…

We revisit the selection problem, namely that of computing the $i$th order statistic of $n$ given elements, in particular the classic deterministic algorithm by grouping and partition due to Blum, Floyd, Pratt, Rivest, and Tarjan (1973).…

In the graph clustering problem with a planted solution, the input is a graph on $n$ vertices partitioned into $k$ clusters, and the task is to infer the clusters from graph structure. A standard assumption is that clusters induce…

We introduce a new family of priority-queue data structures: partition-based simple heaps. The structures consist of $O(\log n)$ doubly-linked lists; order is enforced among data in different lists, but the individual lists are unordered.…

Let ${R} = \{R_1, R_2, ..., R_n\}$ be a set of regions and let $ X = \{x_1, x_2, ..., x_n\}$ be an (unknown) point set with $x_i \in R_i$. Region $R_i$ represents the uncertainty region of $x_i$. We consider the following question: how fast…

In this paper we study the Prefix Sum problem introduced by Fredman. We show that it is possible to perform both update and retrieval in O(1) time simultaneously under a memory model in which individual bits may be shared by several words.…

Listing triangles is a fundamental graph problem with many applications, and large graphs require fast algorithms. Vertex ordering allows the orientation of edges from lower to higher vertex indices, and state-of-the-art triangle listing…

We describe and analyze Zig-zag Sort--a deterministic data-oblivious sorting algorithm running in O(n log n) time that is arguably simpler than previously known algorithms with similar properties, which are based on the AKS sorting network.…

We give algorithms with running time $2^{O({\sqrt{k}\log{k}})} \cdot n^{O(1)}$ for the following problems. Given an $n$-vertex unit disk graph $G$ and an integer $k$, decide whether $G$ contains (1) a path on exactly/at least $k$ vertices,…

Bitmap indexes must be compressed to reduce input/output costs and minimize CPU usage. To accelerate logical operations (AND, OR, XOR) over bitmaps, we use techniques based on run-length encoding (RLE), such as Word-Aligned Hybrid (WAH)…

Discovering the underlying structure of a given graph is one of the fundamental goals in graph mining. Given a graph, we can often order vertices in a way that neighboring vertices have a higher probability of being connected to each other.…

Planar graphs are known to allow subexponential algorithms running in time $2^{O(\sqrt n)}$ or $2^{O(\sqrt n \log n)}$ for most of the paradigmatic problems, while the brute-force time $2^{\Theta(n)}$ is very likely to be asymptotically…

We empirically study sorting in the evolving data model. In this model, a sorting algorithm maintains an approximation to the sorted order of a list of data items while simultaneously, with each comparison made by the algorithm, an…

In this paper we further investigate the well-studied problem of finding a perfect matching in a regular bipartite graph. The first non-trivial algorithm, with running time $O(mn)$, dates back to K\"{o}nig's work in 1916 (here $m=nd$ is the…

Given in the plane a set of points and a set of halfplanes, we consider the problem of computing a smallest subset of halfplanes whose union covers all points. In this paper, we present an $O(n^{4/3}\log^{5/3}n\log^{O(1)}\log n)$-time…