数据结构与算法

The problem of subgraph counting asks for the number of occurrences of a pattern graph $H$ as a subgraph of a host graph $G$ and is known to be computationally challenging: it is $\#W[1]$-hard even when $H$ is restricted to simple…

Interest in the random-order model (ROM) leads us to initiate a study of utilizing random-order arrivals to extract random bits with the goal of derandomizing algorithms. Besides producing simple algorithms, simulating random bits through…

For databases consisting of many text documents, one of the most fundamental data analysis tasks is counting (i) how often a pattern appears as a substring in the database (substring counting) and (ii) how many documents in the collection…

The freight industry is undergoing a digital revolution, with an ever-growing volume of transactions being facilitated by digital marketplaces. A core capability of these marketplaces is the fulfillment of demand for truckload movements…

Fault-tolerant spanners are fundamental objects that preserve distances in graphs even under edge failures. A long line of work culminating in Bodwin, Dinitz, Robelle (SODA 2022) gives $(2k-1)$-stretch, $f$-fault-tolerant spanners with…

A large number of NP-hard graph problems can be solved in $f(w)n^{O(1)}$ time and space when the input graph is provided together with a tree decomposition of width $w$, in many cases with a modest exponential dependence $f(w)$ on $w$.…

Given a finite metric space $(X\cup Y, \mathbf{d})$ the $k$-median problem is to find a set of $k$ centers $C\subseteq Y$ that minimizes $\sum_{p\in X} \min_{c\in C} \mathbf{d}(p,c)$. In general metrics, the best polynomial time algorithm…

This article provides a survey of circuit complexity bounds for basic boolean transforms exploited in digital circuit design and efficient methods for synthesizing such circuits. The exposition covers structurally simple functions and…

In this work, we focus on designing an efficient Local Computation Algorithm (LCA) for the set cover problem, which is a core optimization task. The state-of-the-art LCA for computing $O(\log \Delta)$-approximate set cover, developed by…

The $k$-of-$n$ testing problem involves performing $n$ independent tests sequentially, in order to determine whether/not at least $k$ tests pass. The objective is to minimize the expected cost of testing. This is a fundamental and…

We develop the first algorithms for computing the Skyscraper Invariant [FJNT24]. This is a filtration of the classical rank invariant for multiparameter persistence modules defined by the Harder-Narasimhan filtrations along every central…

Motivated by evacuation scenarios arising in extreme events such as flooding or forest fires, we study the problem of smoothly scheduling a set of paths in graphs where connections become impassable at some point in time. A schedule is…

Given a tree, a set of pebbles initially stationed at some nodes of the tree, and a set of target nodes, the Unlabeled Pebble Motion on Trees problem (UPMT) asks to find a plan to move the pebbles one-at-a-time from the starting nodes to…

DRESS is a deterministic, parameter-free framework for structural graph refinement that iteratively refines the structural similarity of edges in a graph to produce a canonical fingerprint: a real-valued edge vector, obtained by converging…

The $L_2$-norm, or collision norm, is a core entity in the analysis of distributions and probabilistic algorithms. Batu and Canonne (FOCS 2017) presented an extensive analysis of algorithmic aspects of the $L_2$-norm and its connection to…

Let $G=(V,E)$ be an undirected unweighted multi-graph and $S\subseteq V$ be a subset of vertices. A set of edges with the least cardinality whose removal disconnects $S$, that is, there is no path between at least one pair of vertices from…

Reconfiguration problems involve determining whether two given configurations can be transformed into each other under specific rules. The Token Sliding problem asks whether, given two different set of tokens on vertices of a graph $G$, we…

The $k$-center problem is a fundamental clustering variant with applications in learning systems and data summarization. In several real-world scenarios, the dataset to be clustered is not static, but evolves over time, as new data points…

We study the problem of constructing a dynamic fully indexable dictionary (FID) in the Word-RAM model using space close to the information-theoretic lower bound. A FID is a data-structure that encodes a bit-vector $B$ of length $u$ and…

The Maximum Common Subgraph (MCS) problem plays a key role in many applications, including cheminformatics, bioinformatics, and pattern recognition, where it is used to identify the largest shared substructure between two graphs. Although…