My research focuses on designing new distributed and parallel algorithms, the distributed processing of big data, achieving fault-tolerance in communication networks against adversarial attacks, and developing robust protocols that work in highly dynamic environments such as peer-to-peer Blockchain networks and mobile ad-hoc networks.

## Publications

2019
• The Complexity of Symmetry Breaking in Massive Graphs.DOI
Christian Konrad, Sriram V. Pemmaraju, Talal Riaz, and Peter Robinson. 32nd International Symposium on Distributed Computing LIPIcs, Vol. 146 (DISC 2019).
2018
• On the Distributed Complexity of Large-Scale Graph ComputationsDOI
Gopal Pandurangan, Peter Robinson, Michele Scquizzato. 30th ACM Symposium on Parallelism in Algorithms and Architectures. (SPAA 2018).
Abstract
Motivated 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.
• Fast Distributed Algorithms for Connectivity and MST in Large Graphs
Gopal Pandurangan, Peter Robinson, Michele Scquizzato. Special Issue of ACM Transactions on Parallel Computing. (TOPC).
Abstract
Motivated 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.
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).
Abstract
Motivated 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).
Abstract
Motivated 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.

## Code

I'm interested in parallel and distributed programming and related technologies such as software transactional memory and the actor-model. Recently, I have been working on implementing a simulation environment for distributed algorithms in Elixir/Erlang, and implementing non-blocking data structures in Haskell suitable for multi-core machines. Below is a (non-comprehensive) list of software that I have written.
• concurrent hash table: a thread-safe hash table that scales to multicores.
• 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.
• I extended Haskell's Cabal, for using a "world" file to keep track of installed packages. (Now part of the main distribution.)

## Teaching

• CAS781 Randomized Algorithms, Fall 2018: More slides.Intro slides.
• CS5860 Advanced Distributed Systems, Fall 2016, 2017.
• CS5800 Computation with Data, Fall 2016.
• BI5632 Internet and Web Technologies, Spring 2016.
• CSC2008 Networks and Communications, Fall 2015.