数据结构与算法

In Path Set Packing, the input is an undirected graph $G$, a collection $\calp$ of simple paths in $G$, and a positive integer $k$. The problem is to decide whether there exist $k$ edge-disjoint paths in $\calp$. We study the parameterized…

Given a positive integer $d$, the d-CUT is the problem of deciding if an undirected graph $G=(V,E)$ has a cut $(A,B)$ such that every vertex in $A$ (resp. $B$) has at most $d$ neighbors in $B$ (resp. $A$). For $d=1$, the problem is referred…

We investigate an AND-OR tree T and a probability distribution d on the truth assignments to the leaves. Tarsi (1983) showed that if d is an independent and identical distribution (IID) such that probability of a leaf having value 0 is…

We prove that every graph has a spectral sparsifier with a number of edges linear in its number of vertices. As linear-sized spectral sparsifiers of complete graphs are expanders, our sparsifiers of arbitrary graphs can be viewed as…

Maximizing monotone submodular functions under cardinality constraints is a classic optimization task with several applications in data mining and machine learning. In this paper we study this problem in a dynamic environment with…

The challenge of estimating similarity between sets has been a significant concern in data science, finding diverse applications across various domains. However, previous approaches, such as MinHash, have predominantly centered around…

Neural embedding models have become a fundamental component of modern information retrieval (IR) pipelines. These models produce a single embedding $x \in \mathbb{R}^d$ per data-point, allowing for fast retrieval via highly optimized…

We report on experiments with the ziggurat algorithm for generating Gaussian distributed random numbers. The study utilizes our open source Java implementation that was introduced originally for Java 11 at a time when the Java API only…

We consider the feedback vertex set problem in undirected graphs (FVS). The input to FVS is an undirected graph $G=(V,E)$ with non-negative vertex costs. The goal is to find a minimum cost subset of vertices $S \subseteq V$ such that $G-S$…

We study the parameterized complexity of finding shortest s-t-paths with an additional fairness requirement. The task is to compute a shortest path in a vertex-colored graph where each color appears (roughly) equally often in the solution.…

The tango tree is the first proven $O(\lg \lg n)$-competitive binary search tree (BST). We present the first ever experimental implementation of tango trees and compare the running time of the tango tree with the multi-splay tree and the…

Push-Relabel is one of the most celebrated network flow algorithms. Maintaining a pre-flow that saturates a cut, it enjoys better theoretical and empirical running time than other flow algorithms, such as Ford-Fulkerson. In practice,…

Given a set of customers, the Flying Sidekick Traveling Salesman Problem (FSTSP) consists of using one truck and one drone to perform deliveries to them. The drone is limited to delivering to one customer at a time, after which it returns…

In this work, we give a new technique for analyzing individualized privacy accounting via the following simple observation: if an algorithm is one-sided add-DP, then its subsampled variant satisfies two-sided DP. From this, we obtain…

In this paper we study the problem of finding $(\epsilon, \phi)$-expander decompositions of a graph in the streaming model, in particular for dynamic streams of edge insertions and deletions. The goal is to partition the vertex set so that…

Coloring is a notoriously hard problem, and even more so in the online setting, where each arriving vertex has to be colored immediately and irrevocably. Already on trees, which are trivially two-colorable, it is impossible to achieve…

How should we thread a single string through a set of tubes so that pulling the string taut self-assembles the tubes into a desired graph? While prior work [ITCS 2024] solves this problem with the goal of minimizing the length of string, we…

Cardinality sketches are popular data structures that enhance the efficiency of working with large data sets. The sketches are randomized representations of sets that are only of logarithmic size but can support set merges and approximate…

In this paper we study the Product Partition Problem (PPP), i.e. we are given a set of $n$ natural numbers represented on $m$ bits each and we are asked if a subset exists such that the product of the numbers in the subset equals the…

Inspired by artistic practices such as beadwork and himmeli, we study the problem of threading a single string through a set of tubes, so that pulling the string forms a desired graph. More precisely, given a connected graph (where edges…