## Peter Robinson

I'm an Assistant Professor (UK Lecturer) at Royal Holloway, University of London. I'm interested in designing new distributed and parallel algorithms, the distributed processing of big data, achieving fault-tolerance in networks, and secure distributed computing in dynamic environments such as peer-to-peer networks and mobile ad-hoc networks.

## News

- General Chair of ACM PODC 2019
- Publicity Chair of DISC 2018
- Program committee member of PODC 2018, DISC 2018, ICDCS 2018, BGP 2017, SPAA 2016
- Presentation at the workshop on Dynamic Graphs in Distributed Computing (co-located with DISC 2016)
- Program Committee Co-Chair of ICDCN 2016
- Presentation at ADGA 2015, (4th Workshop on Advances in Distributed Graph Algorithms, co-located with DISC 2015)

## Keywords (Show all)

Asynchrony Big Data Byzantine Failures Churn Communication Complexity Distributed Agreement Distributed Storage Dynamic Network Fault-Tolerance Gossip Communication Graph Algorithm Haskell Leader Election Machine Learning Mobile Ad-Hoc Network Natural Language Processing P2P Secure Computation Self-Healing Symmetry Breaking## Publications

2017

- Tight Bounds for Distributed Graph ComputationsDOI

Gopal Pandurangan, Peter Robinson, Michele Scquizzato. (under review)

AbstractMotivated by the need to understand the algorithmic foundations of distributed large-scale graph computations, we study some fundamental graph problems in a message-passing model for distributed computing where $k \geq 2$ machines jointly perform computations on graphs with $n$ nodes (typically, $n \gg k$). The input graph is assumed to be initially randomly partitioned among the $k$ machines, a common implementation in many real-world systems. Communication is point-to-point, and the goal is to minimize the number of communication rounds of the computation. We present (almost) tight bounds for the round complexity of two fundamental graph problems, namely triangle enumeration and PageRank computation. Our tight lower bounds, a main contribution of the paper, are established through an information-theoretic approach that relates the round complexity to the minimal amount of information required by machines for solving a problem. Our approach is generic and can be useful in showing lower bounds in the context of similar problems and similar models. Our approach, as demonstrated in the case of triangle enumeration, can yield stronger round lower bounds as well as message-round tradeoffs compared to approaches that use communication complexity techniques. We then present algorithms that (almost) match the lower bounds; these algorithms exhibit a round complexity which scales superlinearly in $k$, improving significantly over previous results. Specifically, we show the following results: 1. Triangle enumeration: We show that there exist graphs with $m$ edges where any distributed algorithm requires $\tilde{\Omega}(m/k^{5/3})$ rounds. This result implies the first non-trivial lower bound of $\tilde\Omega(n^{1/3})$ rounds for the congested clique model, which is tight up to logarithmic factors. We also present a distributed algorithm that enumerates all the triangles of a graph in $\tilde{O}(m/k^{5/3})$ rounds. 2. PageRank: We show a lower bound of $\tilde{\Omega}(n/k^2)$ rounds, and present a simple distributed algorithm that computes the PageRank of all the nodes of a graph in $\tilde{O}(n/k^2)$ rounds.

2016

- Fast Distributed Algorithms for Connectivity and MST in Large GraphsDOI

Gopal Pandurangan, Peter Robinson, Michele Scquizzato. 28th ACM Symposium on Parallelism in Algorithms and Architectures (SPAA 2016).

AbstractMotivated by the increasing need to understand the algorithmic foundations of distributed large-scale graph computations, we study a number of fundamental graph problems in a message-passing model for distributed computing where $k \geq 2$ machines jointly perform computations on graphs with $n$ nodes (typically, $n \gg k$). The input graph is assumed to be initially randomly partitioned among the $k$ machines, a common implementation in many real-world systems. Communication is point-to-point, and the goal is to minimize the number of communication rounds of the computation. Our main result is an (almost) optimal distributed randomized algorithm for graph connectivity. Our algorithm runs in $\tilde{O}(n/k^2)$ rounds ($\tilde{O}$ notation hides a $\text{polylog}(n)$ factor and an additive $\text{polylog}(n)$ term). This improves over the best previously known bound of $\tilde{O}(n/k)$ [Klauck et al., SODA 2015], and is optimal (up to a polylogarithmic factor) in view of an existing lower bound of $\tilde{\Omega}(n/k^2)$. Our improved algorithm uses a bunch of techniques, including linear graph sketching, that prove useful in the design of efficient distributed graph algorithms. We then present fast randomized algorithms for computing minimum spanning trees, (approximate) min-cuts, and for many graph verification problems. All these algorithms take $\tilde{O}(n/k^2)$ rounds, and are optimal up to polylogarithmic factors. We also show an almost matching lower bound of $\tilde{\Omega}(n/k^2)$ for many graph verification problems using lower bounds in random-partition communication complexity.

2015

- Distributed Computation of Large-scale Graph ProblemsPDFDOI

Hartmut Klauck, Danupon Nanongkai, Gopal Pandurangan, Peter Robinson. 26th ACM-SIAM Symposium on Discrete Algorithms (SODA 2015).

AbstractMotivated by the increasing need for fast distributed processing of large-scale graphs such as the Web graph and various social networks, we study a number of fundamental graph problems in the message-passing model, where we have $k$ machines that jointly perform computation on an arbitrary $n$-node (typically, $n \gg k$) input graph. The graph is assumed to be randomly partitioned among the $k \geq 2$ machines (a common implementation in many real world systems). The communication is point-to-point, and the goal is to minimize the time complexity, i.e., the number of communication rounds, of solving various fundamental graph problems. We present lower bounds that quantify the fundamental time limitations of distributively solving graph problems. We first show a lower bound of $\Omega(n/k)$ rounds for computing a spanning tree (ST) of the input graph. This result also implies the same bound for other fundamental problems such as computing a minimum spanning tree (MST), breadth-first tree (BFS), and shortest paths tree (SPT). We also show an $\Omega(n/k^2)$ lower bound for connectivity, ST verification and other related problems. Our lower bounds develop and use new bounds in random-partition communication complexity. To complement our lower bounds, we also give algorithms for various fundamental graph problems, e.g., PageRank, MST, connectivity, ST verification, shortest paths, cuts, spanners, covering problems, densest subgraph, subgraph isomorphism, finding triangles, etc. We show that problems such as PageRank, MST, connectivity, and graph covering can be solved in $\tilde{O}(n/k)$ time (the notation $\tilde O$ hides $\text{polylog}(n)$ factors and an additive $\text{polylog}(n)$ term); this shows that one can achieve almost linear (in $k$) speedup, whereas for shortest paths, we present algorithms that run in $\tilde{O}(n/\sqrt{k})$ time (for $(1+\epsilon)$-factor approximation) and in $\tilde{O}(n/k)$ time (for $O(\log n)$-factor approximation) respectively. Our results are a step towards understanding the complexity of distributively solving large-scale graph problems.

2014

- Distributed Symmetry Breaking in HypergraphsPDFDOI

Shay Kutten, Danupon Nanongkai, Gopal Pandurangan, Peter Robinson. 28th International Symposium on Distributed Computing (DISC 2014).

AbstractFundamental local symmetry breaking problems such as Maximal Independent Set (MIS) and coloring have been recognized as important by the community, and studied extensively in (standard) graphs. In particular, fast (i.e., logarithmic run time) randomized algorithms are well-established for MIS and $\Delta +1$-coloring in both the LOCAL and CONGEST distributed computing models. On the other hand, comparatively much less is known on the complexity of distributed symmetry breaking in hypergraphs. In particular, a key question is whether a fast (randomized) algorithm for MIS exists for hypergraphs. In this paper, we study the distributed complexity of symmetry breaking in hypergraphs by presenting distributed randomized algorithms for a variety of fundamental problems under a natural distributed computing model for hypergraphs. We first show that MIS in hypergraphs (of arbitrary dimension) can be solved in $O(\log^2 n)$ rounds ($n$ is the number of nodes of the hypergraph) in the LOCAL model. We then present a key result of this paper --- an $O(\Delta^{\epsilon}\text{poly} \log n)$-round hypergraph MIS algorithm in the CONGEST model where $\Delta$ is the maximum node degree of the hypergraph and $\epsilon > 0$ is any arbitrarily small constant. To demonstrate the usefulness of hypergraph MIS, we present applications of our hypergraph algorithm to solving problems in (standard) graphs. In particular, the hypergraph MIS yields fast distributed algorithms for the balanced minimal dominating set problem (left open in Harris et al. [ICALP 2013]) and the minimal connected dominating set problem. We also present distributed algorithms for coloring, maximal matching, and maximal clique in hypergraphs. Our work shows that while some local symmetry breaking problems such as coloring can be solved in polylogarithmic rounds in both the LOCAL and CONGEST models, for many other hypergraph problems such as MIS, hitting set, and maximal clique, it remains challenging to obtain polylogarithmic time algorithms in the CONGEST model. This work is a step towards understanding this dichotomy in the complexity of hypergraph problems as well as using hypergraphs to design fast distributed algorithms for problems in (standard) graphs.

## Code

I'm interested in parallel and distributed programming and related technologies such as software transactional memory. Below is a (non-comprehensive) list of software that I have written.

- I extended Haskell's Cabal, for using a "world" file to keep track of installed packages. (Now part of the main distribution.)
- data dispersal: an implementation of an (m,n)-threshold information dispersal scheme that is space-optimal.
- secret sharing: an implementation of a secret sharing scheme that provides information-theoretic security.
- tskiplist: a data structure with range-query support for software transactional memory.
- stm-io-hooks: An extension of Haskell's Software Transactional Memory (STM) monad with commit and retry IO hooks.
- Mathgenealogy: Visualize your (academic) genealogy! A program for extracting data from the Mathematics Genealogy project.
- In my master thesis I developed a system for automatically constructing events out of log files produced by various system programs. One of the core components of my work was a part-of-speech (POS) tagger, which assigns word classes (e.g. noun, verb) to the previously parsed tokens of the log file. To cope with noisy input data, I modeled the POS tagger as a hidden Markov model. I developed (and proved the correctness of) a variant of the maximum likelihood estimation algorithm for training the Markov model and smoothing the state transition distributions.

## Misc

- On program committee of: PODC 2018, BGP 2017, ICDCN 2016, SPAA 2016, SIROCCO 2016, ICDCN 2015, SIROCCO 2014, FOMC 2014.
- DBLP entry (Shows a subset of my publications.)
- Google scholar profile
- My profile on StackExchange