数据结构与算法

We consider the classical online bipartite matching problem in the probe-commit model. In this problem, when an online vertex arrives, its edges must be probed to determine if they exist, based on known edge probabilities. A probing…

In this paper, we present a neural network-enabled data distribution aware sorting method, coined as NN-sort. Our approach explores the potential of developing deep learning techniques to speed up large-scale sort operations, enabling data…

The Domain Name System (DNS) plays a critical role in the functioning of the Internet. It provides a hierarchical name space for locating resources. Data is typically stored in plain text files, possibly spanning gigabytes. Frequent parsing…

We consider the matching problem on the line with advice complexity. We give a 1-competitive online algorithm with advice complexity $n-1,$ and show that there is no 1-competitive online algorithm reading less than $n-1$ bits of advice.…

The Steiner Forest problem is an important generalization of the Steiner Tree problem. We are given an undirected graph with nonnegative edge costs and a collection of pairs of vertices. The task is to compute a cheapest forest with the…

We describe the implementation of the exact solver weberknecht and the heuristic solver weberknecht_h for the One-Sided Crossing Minimization problem.

In this paper we propose a linear-time certifying algorithm for the single-source shortest-path problem capable of verifying graphs with positive, negative, and zero arc weights. Previously proposed linear-time approaches only work for…

In the adversarial streaming model, the input is a sequence of adaptive updates that defines an underlying dataset and the goal is to approximate, collect, or compute some statistic while using space sublinear in the size of the dataset. In…

Path planning is a fundamental problem in road networks, with the goal of finding a path that optimizes objectives such as shortest distance or minimal travel time. Existing methods typically use graph indexing to ensure the efficiency of…

We consider the problem of finding an independent set of maximum weight simultaneously contained in $k$ matroids over a common ground set. This $k$-matroid intersection problem appears naturally in many contexts, for example in generalizing…

The textbook algorithm for single-source shortest paths with real-valued edge weights runs in $O(m n)$ time on a graph with $m$ edges and $n$ vertices. A recent breakthrough algorithm by Fineman [Fin24] takes $\tilde O(m n^{8/9})$…

We consider the problem of efficiently solving a system of $n$ non-linear equations in ${\mathbb R}^d$. Addressing Smale's 17th problem stated in 1998, we consider a setting whereby the $n$ equations are random homogeneous polynomials of…

We consider succinct data structures for representing a set of $n$ horizontal line segments in the plane given in rank space to support \emph{segment access}, \emph{segment selection}, and \emph{segment rank} queries. A segment access query…

We consider the problem of finding a minimum cut of a weighted graph presented as a single-pass stream. While graph sparsification in streams has been intensively studied, the specific application of finding minimum cuts in streams is less…

In this paper we further explore the recently discovered connection by Bj\"{o}rklund and Kaski [STOC 2024] and Pratt [STOC 2024] between the asymptotic rank conjecture of Strassen [Progr. Math. 1994] and the three-way partitioning problem.…

We prove a robust contraction decomposition theorem for $H$-minor-free graphs, which states that given an $H$-minor-free graph $G$ and an integer $p$, one can partition in polynomial time the vertices of $G$ into $p$ sets $Z_1,\dots,Z_p$…

In many decision-making processes, one may prefer multiple solutions to a single solution, which allows us to choose an appropriate solution from the set of promising solutions that are found by algorithms. Given this, finding a set of…

Integer division instruction is generally expensive in most architectures. If the divisor is constant, the division can be transformed into combinations of several inexpensive integer instructions. This article discusses the classic…

The problem of determining whether a graph $G$ contains another graph $H$ as a minor, referred to as the minor containment problem, is a fundamental problem in the field of graph algorithms. While it is NP-complete when $G$ and $H$ are…

This paper tightens the best known analysis of Hein's 1989 algorithm to infer the topology of a weighted tree based on the lengths of paths between its leaves. It shows that the number of length queries required for a degree-$k$ tree of $n$…