Seth Pettie
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View article: A Refutation of the Pach-Tardos Conjecture for 0–1 Matrices
A Refutation of the Pach-Tardos Conjecture for 0–1 Matrices Open
The theory of forbidden 0–1 matrices generalizes Turán-style (bipartite) subgraph avoidance, Davenport-Schinzel theory, and Zarankiewicz-type problems, and has been influential in many areas, such as discrete and computational geometry, th…
View article: Connectivity Labeling Schemes for Edge and Vertex Faults via Expander Hierarchies
Connectivity Labeling Schemes for Edge and Vertex Faults via Expander Hierarchies Open
We consider the problem of assigning short labels to the vertices and edges of a graph $G$ so that given any query $\langle s,t,F\rangle$ with $|F|\leq f$, we can determine whether $s$ and $t$ are still connected in $G-F$, given only the l…
View article: A Refutation of the Pach-Tardos Conjecture for 0-1 Matrices
A Refutation of the Pach-Tardos Conjecture for 0-1 Matrices Open
The theory of forbidden 0-1 matrices generalizes Turan-style (bipartite) subgraph avoidance, Davenport-Schinzel theory, and Zarankiewicz-type problems, and has been influential in many areas, such as discrete and computational geometry, th…
View article: Connectivity Labeling and Routing with Multiple Vertex Failures
Connectivity Labeling and Routing with Multiple Vertex Failures Open
We present succinct labeling schemes for answering connectivity queries in graphs subject to a specified number of vertex failures. An f-vertex/edge fault tolerant (f-V/EFT) connectivity labeling is a scheme that produces succinct labels f…
View article: Connectivity Labeling and Routing with Multiple Vertex Failures
Connectivity Labeling and Routing with Multiple Vertex Failures Open
We present succinct labeling schemes for answering connectivity queries in graphs subject to a specified number of vertex failures. An $f$-vertex/edge fault tolerant ($f$-V/EFT) connectivity labeling is a scheme that produces succinct labe…
View article: On the Extremal Functions of Acyclic Forbidden 0-1 Matrices
On the Extremal Functions of Acyclic Forbidden 0-1 Matrices Open
The extremal theory of forbidden 0-1 matrices studies the asymptotic growth of the function $\mathrm{Ex}(P,n)$, which is the maximum weight of a matrix $A\in\{0,1\}^{n\times n}$ whose submatrices avoid a fixed pattern $P\in\{0,1\}^{k\times…
View article: Fully Dynamic Connectivity in $O(\log n(\log\log n)^2)$ Amortized Expected Time
Fully Dynamic Connectivity in $O(\log n(\log\log n)^2)$ Amortized Expected Time Open
Dynamic connectivity is one of the most fundamental problems in dynamic graph algorithms. We present a randomized Las Vegas dynamic connectivity data structure with $O(\log n(\log\log n)^2)$ amortized expected update time and $O(\log n/\lo…
View article: Byzantine Agreement with Optimal Resilience via Statistical Fraud Detection
Byzantine Agreement with Optimal Resilience via Statistical Fraud Detection Open
Since the mid-1980s it has been known that Byzantine Agreement can be solved with probability 1 asynchronously, even against an omniscient, computationally unbounded adversary that can adaptively \emph{corrupt} up to $f
View article: Byzantine Agreement in Polynomial Time with Near-Optimal Resilience
Byzantine Agreement in Polynomial Time with Near-Optimal Resilience Open
It has been known since the early 1980s that Byzantine Agreement in the full information, asynchronous model is impossible to solve deterministically against even one crash fault [FLP85], but that it can be solved with probability 1 [Ben83…
View article: Space Complexity of Vertex Connectivity Oracles
Space Complexity of Vertex Connectivity Oracles Open
A $k$-vertex connectivity oracle for undirected $G$ is a data structure that, given $u,v\in V(G)$, reports $\min\{k,κ(u,v)\}$, where $κ(u,v)$ is the pairwise vertex connectivity between $u,v$. There are three main measures of efficiency: c…
View article: Near-Optimal Distributed Computation of Small Vertex Cuts
Near-Optimal Distributed Computation of Small Vertex Cuts Open
We present near-optimal algorithms for detecting small vertex cuts in the {CONGEST} model of distributed computing. Despite extensive research in this area, our understanding of the vertex connectivity of a graph is still incomplete, espec…
View article: Near-optimal Distributed Triangle Enumeration via Expander Decompositions
Near-optimal Distributed Triangle Enumeration via Expander Decompositions Open
We present improved distributed algorithms for variants of the triangle finding problem in the model. We show that triangle detection, counting, and enumeration can be solved in rounds using expander decompositions . This matches the trian…
View article: Incremental SCC Maintenance in Sparse Graphs
Incremental SCC Maintenance in Sparse Graphs Open
In the incremental cycle detection problem, edges are added to a directed graph (initially empty), and the algorithm has to report the presence of the first cycle, once it is formed. A closely related problem is the incremental topological…
View article: Non-Mergeable Sketching for Cardinality Estimation
Non-Mergeable Sketching for Cardinality Estimation Open
Cardinality estimation is perhaps the simplest non-trivial statistical problem that can be solved via sketching. Industrially-deployed sketches like HyperLogLog, MinHash, and PCSA are mergeable, which means that large data sets can be sket…
View article: Planar Distance Oracles with Better Time-Space Tradeoffs
Planar Distance Oracles with Better Time-Space Tradeoffs Open
In a recent breakthrough, Charalampopoulos, Gawrychowski, Mozes, and Weimann [9] showed that exact distance queries on planar graphs could be answered in no(1) time by a data structure occupying n1+o(1) space, i.e., up to o(1) terms, optim…
View article: The Structure of Minimum Vertex Cuts
The Structure of Minimum Vertex Cuts Open
In this paper we continue a long line of work on representing the cut structure of graphs. We classify the types of minimum vertex cuts, and the possible relationships between multiple minimum vertex cuts. As a consequence of these investi…
View article: The Communication Complexity of Set Intersection and Multiple Equality Testing
The Communication Complexity of Set Intersection and Multiple Equality Testing Open
In this paper we explore fundamental problems in randomized communication complexity such as computing Set Intersection on sets of size $k$ and Equality Testing between vectors of length $k$. Sağlam and Tardos and Brody et al. showed that …
View article: Wake up and Join Me! an Energy-Efficient Algorithm for Maximal Matching in Radio Networks
Wake up and Join Me! an Energy-Efficient Algorithm for Maximal Matching in Radio Networks Open
We consider networks of small, autonomous devices that communicate with each other wirelessly. Minimizing energy usage is an important consideration in designing algorithms for such networks, as battery life is a crucial and limited resour…
View article: Simple and Efficient Cardinality Estimation in Data Streams.
Simple and Efficient Cardinality Estimation in Data Streams. Open
We study sketching schemes for the cardinality estimation problem in data streams, and advocate for measuring the efficiency of such a scheme in terms of its MVP: Memory-Variance Product, i.e., the product of its space, in bits, and the re…
View article: The Energy Complexity of BFS in Radio Networks
The Energy Complexity of BFS in Radio Networks Open
We consider a model of energy complexity in Radio Networks in which transmitting or listening on the channel costs one unit of energy and computation is free. This simplified model captures key aspects of battery-powered sensors: that batt…
View article: The Energy Complexity of BFS in Radio Networks
The Energy Complexity of BFS in Radio Networks Open
We consider a model of energy complexity in Radio Networks in which transmitting or listening on the channel costs one unit of energy and computation is free. This simplified model captures key aspects of battery-powered sensors: that batt…
View article: Planar Distance Oracles with Better Time-Space Tradeoffs
Planar Distance Oracles with Better Time-Space Tradeoffs Open
In a recent breakthrough, Charalampopoulos, Gawrychowski, Mozes, and Weimann (STOC 2019) showed that exact distance queries on planar graphs could be answered in $n^{o(1)}$ time by a data structure occupying $n^{1+o(1)}$ space, i.e., up to…
View article: Information Theoretic Limits of Cardinality Estimation: Fisher Meets Shannon
Information Theoretic Limits of Cardinality Estimation: Fisher Meets Shannon Open
Estimating the cardinality (number of distinct elements) of a large multiset is a classic problem in streaming and sketching, dating back to Flajolet and Martin's classic Probabilistic Counting (PCSA) algorithm from 1983. In this paper we …
View article: Contention resolution without collision detection
Contention resolution without collision detection Open
This paper focuses on the contention resolution problem on a shared communication channel that does not support collision detection. A shared communication channel is a multiple access channel, which consists of a sequence of synchronized …
View article: The Communication Complexity of Set Intersection and Multiple Equality Testing
The Communication Complexity of Set Intersection and Multiple Equality Testing Open
In this paper we explore fundamental problems in randomized communication complexity such as computing Set Intersection on sets of size $k$ and Equality Testing between vectors of length $k$. Sa\u{g}lam and Tardos and Brody et al. showed t…
View article: Joins on Samples: A Theoretical Guide for Practitioners
Joins on Samples: A Theoretical Guide for Practitioners Open
Despite decades of research on approximate query processing (AQP), our understanding of sample-based joins has remained limited and, to some extent, even superficial. The common belief in the community is that joining random samples is fut…
View article: Distributed Edge Coloring and a Special Case of the Constructive Lovász Local Lemma
Distributed Edge Coloring and a Special Case of the Constructive Lovász Local Lemma Open
The complexity of distributed edge coloring depends heavily on the palette size as a function of the maximum degree Δ. In this article, we explore the complexity of edge coloring in the LOCAL model in different palette size regimes. Our re…
View article: Exponential Separations in the Energy Complexity of Leader Election
Exponential Separations in the Energy Complexity of Leader Election Open
Energy is often the most constrained resource for battery-powered wireless devices, and most of the energy is often spent on transceiver usage (i.e., transmitting and receiving packets) rather than computation. In this article, we study th…
View article: Distributed triangle detection via expander decomposition
Distributed triangle detection via expander decomposition Open
We present improved distributed algorithms for triangle detection and its variants in the CONGEST model. We show that Triangle Detection, Counting, and Enumeration can be solved in O(n1/2) rounds. In contrast, the previous state-of-the-art…