Anthony Wirth
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$O(1)$-Round MPC Algorithms for Multi-dimensional Grid Graph Connectivity, EMST and DBSCAN Open
In this paper, we investigate three fundamental problems in the Massively Parallel Computation (MPC) model: (i) grid graph connectivity, (ii) approximate Euclidean Minimum Spanning Tree (EMST), and (iii) approximate DBSCAN. Our first resul…
Optimal Dynamic Parameterized Subset Sampling Open
In this paper, we study the Dynamic Parameterized Subset Sampling (DPSS) problem in the Word RAM model. In DPSS, the input is a set, S , of n items, where each item, x , has a non-negative integer weight, w(x). Given a pair of query parame…
Optimal Dynamic Parameterized Subset Sampling Open
In this paper, we study the Dynamic Parameterized Subset Sampling (DPSS) problem in the Word RAM model. In DPSS, the input is a set,~$S$, of~$n$ items, where each item,~$x$, has a non-negative integer weight,~$w(x)$. Given a pair of query …
Lower Bounds for Approximate (& Exact) k-Disjoint-Shortest-Paths Open
Given a graph $G=(V,E)$ and a set $T=\{ (s_i, t_i) : 1\leq i\leq k \}\subseteq V\times V$ of $k$ pairs, the $k$-vertex-disjoint-paths (resp. $k$-edge-disjoint-paths) problem asks to determine whether there exist~$k$ pairwise vertex-disjoin…
Online Computation of String Net Frequency Open
The net frequency (NF) of a string, of length $m$, in a text, of length $n$, is the number of occurrences of the string in the text with unique left and right extensions. Recently, Guo et al. [CPM 2024] showed that NF is combinatorially in…
Maximum Unique Coverage on Streams: Improved FPT Approximation Scheme and Tighter Space Lower Bound Open
We consider the Max Unique Coverage problem, including applications to the data stream model. The input is a universe of $n$ elements, a collection of $m$ subsets of this universe, and a cardinality constraint, $k$. The goal is to select a…
Exploiting New Properties of String Net Frequency for Efficient Computation Open
Knowing which strings in a massive text are significant -- that is, which strings are common and distinct from other strings -- is valuable for several applications, including text compression and tokenization. Frequency in itself is not h…
Improved Algorithms for Maximum Coverage in Dynamic and Random Order Streams Open
The maximum coverage problem is to select k sets, from a collection of m sets, such that the cardinality of their union, in a universe of size n, is maximized. We consider (1-1/e-ε)-approximation algorithms for this NP-hard problem in thre…
Fast Parallel Algorithms for Submodular $p$-Superseparable Maximization Open
Maximizing a non-negative, monontone, submodular function $f$ over $n$ elements under a cardinality constraint $k$ (SMCC) is a well-studied NP-hard problem. It has important applications in, e.g., machine learning and influence maximizatio…
Sublinear-Space Streaming Algorithms for Estimating Graph Parameters on Sparse Graphs Open
In this paper, we design sub-linear space streaming algorithms for estimating three fundamental parameters -- maximum independent set, minimum dominating set and maximum matching -- on sparse graph classes, i.e., graphs which satisfy $m=O(…
Maximum Coverage in Sublinear Space, Faster Open
Given a collection of $m$ sets from a universe $\mathcal{U}$, the Maximum Set Coverage problem consists of finding $k$ sets whose union has largest cardinality. This problem is NP-Hard, but the solution can be approximated by a polynomial …
View article: Tight Data Access Bounds for Private Top-$k$ Selection
Tight Data Access Bounds for Private Top-$k$ Selection Open
We study the top-$k$ selection problem under the differential privacy model: $m$ items are rated according to votes of a set of clients. We consider a setting in which algorithms can retrieve data via a sequence of accesses, each either a …
Single Round-trip Hierarchical ORAM via Succinct Indices Open
Access patterns to data stored remotely create a side channel that is known to leak information even if the content of the data is encrypted. To protect against access pattern leakage, Oblivious RAM is a cryptographic primitive that obscur…
Walking to Hide: Privacy Amplification via Random Message Exchanges in Network Open
The *shuffle model* is a powerful tool to amplify the privacy guarantees of the *local model* of differential privacy. In contrast to the fully decentralized manner of guaranteeing privacy in the local model, the shuffle model requires a c…
Randomize the Future: Asymptotically Optimal Locally Private Frequency Estimation Protocol for Longitudinal Data Open
Longitudinal data tracking under Local Differential Privacy (LDP) is a challenging task. Baseline solutions that repeatedly invoke a protocol designed for one-time computation lead to linear decay in the privacy or utility guarantee with r…
Dynamic Structural Clustering on Graphs Open
Structural Clustering ($DynClu$) is one of the most popular graph clustering paradigms. In this paper, we consider $StrClu$ under two commonly adapted similarities, namely Jaccard similarity and cosine similarity on a dynamic graph, $G = \…
Asymptotically Optimal Locally Private Heavy Hitters via Parameterized Sketches Open
We present two new local differentially private algorithms for frequency estimation. One solves the fundamental frequency oracle problem; the other solves the well-known heavy hitters identification problem. Consistent with prior art, thes…
Locally Differentially Private Frequency Estimation. Open
We present two new local differentially private algorithms for frequency estimation. One solves the fundamental frequency oracle problem; the other solves the well-known heavy hitters identification problem. Consistent with prior art, thes…
Correlation Clustering in Data Streams Open
Clustering is a fundamental tool for analyzing large data sets. A rich body of work has been devoted to designing data-stream algorithms for the relevant optimization problems such as k -center, k -median, and k -means. Such algorithms nee…
Graph clustering in all parameter regimes Open
Resolution parameters in graph clustering control the size and structure of clusters formed by solving a parametric objective function. Typically there is more than one meaningful way to cluster a graph, and solving the same objective func…
Parameterized Correlation Clustering in Hypergraphs and Bipartite Graphs Open
Motivated by applications in community detection and dense subgraph discovery, we consider new clustering objectives in hypergraphs and bipartite graphs. These objectives are parameterized by one or more resolution parameters in order to e…
Parameterized Objectives and Algorithms for Clustering Bipartite Graphs and Hypergraphs Open
Motivated by applications in community detection and dense subgraph discovery, we consider new clustering objectives in hypergraphs and bipartite graphs. These objectives are parameterized by one or more resolution parameters in order to e…
Recency Queries with Succinct Representation Open
In the context of the sliding-window set membership problem, and caching policies that require knowledge of item recency, we formalize the problem of Recency on a stream. Informally, the query asks, "when was the last time I saw item x?" E…
Graph Clustering in All Parameter Regimes Open
Resolution parameters in graph clustering control the size and structure of clusters formed by solving a parametric objective function. Typically there is more than one meaningful way to cluster a graph, and solving the same objective func…
Learning Resolution Parameters for Graph Clustering Open
Finding clusters of well-connected nodes in a graph is an extensively studied problem in graph-based data analysis. Because of its many applications, a large number of distinct graph clustering objective functions and algorithms have alrea…
Learning Resolution Parameters for Graph Clustering Open
Finding clusters of well-connected nodes in a graph is an extensively studied problem in graph-based data analysis. Because of its many applications, a large number of distinct graph clustering objective functions and algorithms have alrea…
Metric-Constrained Optimization for Graph Clustering Algorithms Open
We outline a new approach for solving linear programming relaxations of NP-hard graph clustering problems that enforce triangle inequality constraints on output variables. Extensive previous research has shown that solutions to these relax…
Result-Sensitive Binary Search with Noisy Information Open
We describe new algorithms for the predecessor problem in the Noisy Comparison Model. In this problem, given a sorted list L of n (distinct) elements and a query q, we seek the predecessor of q in L: denoted by u, the largest element less …