Population protocols (Angluin et al., PODC 2004) are a formal model of sensor networks consisting of identical mobile devices. When two devices come into the range of each other, they interact and change their states. Computations are infinite sequences of pairwise interactions where the interacting processes are picked by a fair scheduler. A population protocol is well specified if for every initial configuration C of devices and for every fair computation starting at C, all devices eventually agree on a consensus value that only depends on C. If a protocol is well-specified, then it is said to compute the predicate that assigns to each initial configuration its consensus value. The main two verification problems for population protocols are: Is a given protocol well-specified? Does a given protocol compute a given predicate? While the class of predicates computable by population protocols was already established in 2007 (Angluin et al., Distributed Computing), the decidability of the verification problems remained open until 2015, when my colleagues and I finally managed to prove it (Esparza et al., CONCUR 2015, improved version to appear in Acta Informatica). In the talk I report on our results and discuss some new developments. Personal Information Management Systems and Knowledge Integration David Montoya, Thomas Pellissier Tanon, and Serge Abiteboul 1 Engie Ineo & ENS Cachan & Inria 2 ENS Lyon 3 INRIA & ENS Cachan Abstract. Personal data is constantly collected, either voluntarily by users in emails, social media interactions, multimedia objects, calendar items, contacts, etc., or passively by various applications such as GPS of mobile devices, transactions, quantified self sensors, etc. The processing of personal data is complicated by the fact that such data is typically stored in silos with different terminologies/ontologies, formats and access protocoles. Users are more and more loosing control over their data; they are sometimes not even aware of the data collected about them and how it is used. We discuss the new concept of Personal Information Management Systems (PIMS for short) that allows each user to be in a position to manage his/her personal information. Some applications are run directly by the PIMS, so are under direct control of the user. Others are in separate systems, that are willing to share with the PIMS the data they collect about that particular user. In that later case, the PIMS is a system for distributed data management. We argue that the time has come for PIMS even though the approach requires a sharp turn from previous models based on the monetisation of personal data. We consider research issues raised by PIMS, either new or that acquire a new avor in a PIMS context. We also present works on the integration of users data from different sources (such as email messages, calendar, contacts, and location history) into a PIMS. The PIMS we consider is a Knowledge Base System based on Semantic Web standards, notably RDF and schema.org. Some of the knowledge is episodical (typically related to spatio-temporal events) and some is semantic (knowledge that holds irrelative to any such event). Of particular interest is the cross enrichment of these two kinds of knowledge based on the alignment of concepts, e.g., enrichment between a calendar and a geographical map using the location history. The goal is to enable users via the PIMS to query and perform analytics over their personal information within and across different dimensions. Personal data is constantly collected, either voluntarily by users in emails, social media interactions, multimedia objects, calendar items, contacts, etc., or passively by various applications such as GPS of mobile devices, transactions, quantified self sensors, etc. The processing of personal data is complicated by the fact that such data is typically stored in silos with different terminologies/ontologies, formats and access protocoles. Users are more and more loosing control over their data; they are sometimes not even aware of the data collected about them and how it is used. We discuss the new concept of Personal Information Management Systems (PIMS for short) that allows each user to be in a position to manage his/her personal information. Some applications are run directly by the PIMS, so are under direct control of the user. Others are in separate systems, that are willing to share with the PIMS the data they collect about that particular user. In that later case, the PIMS is a system for distributed data management. We argue that the time has come for PIMS even though the approach requires a sharp turn from previous models based on the monetisation of personal data. We consider research issues raised by PIMS, either new or that acquire a new avor in a PIMS context. We also present works on the integration of users data from different sources (such as email messages, calendar, contacts, and location history) into a PIMS. The PIMS we consider is a Knowledge Base System based on Semantic Web standards, notably RDF and schema.org. Some of the knowledge is episodical (typically related to spatio-temporal events) and some is semantic (knowledge that holds irrelative to any such event). Of particular interest is the cross enrichment of these two kinds of knowledge based on the alignment of concepts, e.g., enrichment between a calendar and a geographical map using the location history. The goal is to enable users via the PIMS to query and perform analytics over their personal information within and across different dimensions. Matching and Covering in Streaming Graphs

Distributed Computing

We present O(loglog n) -round algorithms in the Massively Parallel Computation (MPC) model, with O (n) memory per machine, that compute a maximal independent set, a 1+e approximation of maximum matching, and a 2+eapproximation of minimum vertex cover, for any n-vertex graph and any constant \eps>0. These improve the state of the art as follows: Our MIS algorithm leads to a simple O(loglog Δ)-round MIS algorithm in the CONGESTED-CLIQUE model of distributed computing, which improves on the O (√log Δ )-round algorithm of Ghaffari [PODC'17]. Our O(loglog n)-round (1+e)-approximate maximum matching algorithm simplifies or improves on the following prior work: O(log^2log n)-round (1+\eps)-approximation algorithm of Czumaj et al. [STOC'18] and $O(loglog n)-round (1+e)-approximation algorithm of Assadi et al. [arXiv'17]. Our O(loglog n)-round (2+e)-approximate minimum vertex cover algorithm improves on an O(loglog n)-round O(1)-approximation of Assadi et al. [arXiv'17].

https://dl.acm.org/doi/pdf/10.1145/3212734.3212743

Improved Massively Parallel Computation Algorithms for MIS, Matching, and Vertex Cover

There has been significant recent interest in parallel graph processing due to the need to quickly analyze the large graphs available today. Many graph codes have been designed for distributed memory or external memory. However, today even the largest publicly-available real-world graph (the Hyperlink Web graph with over 3.5 billion vertices and 128 billion edges) can fit in the memory of a single commodity multicore server. Nevertheless, most experimental work in the literature report results on much smaller graphs, and the ones for the Hyperlink graph use distributed or external memory. Therefore, it is natural to ask whether we can efficiently solve a broad class of graph problems on this graph in memory. This paper shows that theoretically-efficient parallel graph algorithms can scale to the largest publicly-available graphs using a single machine with a terabyte of RAM, processing them in minutes. We give implementations of theoretically-efficient parallel algorithms for 13 important graph problems. We also present the optimizations and techniques that we used in our implementations, which were crucial in enabling us to process these large graphs quickly. We show that the running times of our implementations outperform existing state-of-the-art implementations on the largest real-world graphs. For many of the problems that we consider, this is the first time they have been solved on graphs at this scale. We provide a publicly-available benchmark suite containing our implementations.

https://dl.acm.org/doi/pdf/10.1145/3210377.3210414

Theoretically Efficient Parallel Graph Algorithms Can Be Fast and Scalable

We study the revenue maximization problem of a seller with n heterogeneous items for sale to a single buyer whose valuation function for sets of items is unknown and drawn from some distribution D. We show that if D is a distribution over subadditive valuations with independent items, then the better of pricing each item separately or pricing only the grand bundle achieves a constant-factor approximation to the revenue of the optimal mechanism. This includes buyers who are k-demand, additive up to a matroid constraint, or additive up to constraints of any downwards-closed set system (and whose values for the individual items are sampled independently), as well as buyers who are fractionally subadditive with item multipliers drawn independently. Our proof makes use of the core-tail decomposition framework developed in prior work showing similar results for the significantly simpler class of additive buyers [LY13, BILW14]. 
In the second part of the paper, we develop a connection between approximately optimal simple mechanisms and approximate revenue monotonicity with respect to buyers' valuations. Revenue non-monotonicity is the phenomenon that sometimes strictly increasing buyers' values for every set can strictly decrease the revenue of the optimal mechanism [HR12]. Using our main result, we derive a bound on how bad this degradation can be (and dub such a bound a proof of approximate revenue monotonicity); we further show that better bounds on approximate monotonicity imply a better analysis of our simple mechanisms.

Simple Mechanisms for a Subadditive Buyer and Applications to Revenue Monotonicity

Any graph with maximum degree Δ admits a proper vertex coloring with Δ + 1 colors that can be found via a simple sequential greedy algorithm in linear time and space. But can one find such a coloring via a sublinear algorithm?We answer this fundamental question in the affirmative for several canonical classes of sublinear algorithms including graph streaming, sublinear time, and massively parallel computation (MPC) algorithms. In particular, we design:• A single-pass semi-streaming algorithm in dynamic streams using O(n) space. The only known semi-streaming algorithm prior to our work was a folklore O(log n)-pass algorithm obtained by simulating classical distributed algorithms in the streaming model.• A sublinear-time algorithm in the standard query model that allows neighbor queries and pair queries using [MATH HERE] time. We further show that any algorithm that outputs a valid coloring with sufficiently large constant probability requires [MATH HERE] time. No non-trivial sublinear time algorithms were known prior to our work.• A parallel algorithm in the massively parallel computation (MPC) model using O(n) memory per machine and O(1) MPC rounds. Our number of rounds significantly improves upon the recent O(log log Δ · log* (n))-round algorithm of Parter [ICALP 2018].At the core of our results is a remarkably simple meta-algorithm for the (Δ + 1) coloring problem: Sample O(log n) colors for each vertex independently and uniformly at random from the Δ + 1 colors; find a proper coloring of the graph using only the sampled colors of each vertex. As our main result, we prove that the sampled set of colors with high probability contains a proper coloring of the input graph. The sublinear algorithms are then obtained by designing efficient algorithms for finding a proper coloring of the graph from the sampled colors in each model.We note that all our upper bound results for (Δ + 1) coloring are either optimal or close to best possible in each model studied. We also establish new lower bounds that rule out the possibility of achieving similar results in these models for the closely related problems of maximal independent set and maximal matching. Collectively, our results highlight a sharp contrast between the complexity of (Δ+1) coloring vs maximal independent set and maximal matching in various models of sublinear computation even though all three problems are solvable by a simple greedy algorithm in the classical setting.

Sublinear algorithms for (Δ + 1) vertex coloring

Graph clustering is a fundamental task in many data-mining and machine-learning pipelines. In particular, identifying a good hierarchical structure is at the same time a fundamental and challenging problem for several applications. The amount of data to analyze is increasing at an astonishing rate each day. Hence there is a need for new solutions to efficiently compute effective hierarchical clusterings on such huge data. The main focus of this paper is on minimum spanning tree (MST) based clusterings. In particular, we propose affinity, a novel hierarchical clustering based on Boruvka's MST algorithm. We prove certain theoretical guarantees for affinity (as well as some other classic algorithms) and show that in practice it is superior to several other state-of-the-art clustering algorithms. Furthermore, we present two MapReduce implementations for affinity. The first one works for the case where the input graph is dense and takes constant rounds. It is based on a Massively Parallel MST algorithm for dense graphs that improves upon the state-of-the-art algorithm of Lattanzi et al. (SPAA 2011). Our second algorithm has no assumption on the density of the input graph and finds the affinity clustering in $O(\log n)$ rounds using Distributed Hash Tables (DHTs). We show experimentally that our algorithms are scalable for huge data sets, e.g., for graphs with trillions of edges.

/pdf/affinity-clustering-hierarchical-clustering-at-scale-29nu8embqv.pdf

Affinity Clustering: Hierarchical Clustering at Scale

The Massively Parallel Computation (MPC) model serves as a common abstraction of many modern large-scale parallel computation frameworks and has recently gained a lot of importance, especially in the context of classic graph problems. In this work, we mainly consider maximal matching and maximal independent set problems in the MPC model.These problems are known to admit efficient MPC algorithms if the space available per machine is near-linear in the number n of nodes. This is not only often significantly more than what we can afford, but also allows for easy if not trivial solutions for sparse graphs---which are common in real-world large-scale graphs. We are, therefore, interested in the low-memory MPC model, where the space per machine is restricted to be strongly sublinear, that is, nδ for any constant 0

https://dl.acm.org/doi/pdf/10.1145/3293611.3331609

Massively Parallel Computation of Matching and MIS in Sparse Graphs

We present the first algorithm for maintaining a maximal independent set (MIS) of a fully dynamic graph---which undergoes both edge insertions and deletions---in polylogarithmic time. Our algorithm is randomized and, per update, takes O(log^2 Δ log^2 n) expected time. Furthermore, the algorithm can be adjusted to have O(log^2 Δ log^4 n) worst-case update-time with high probability. Here, n denotes the number of vertices and Δ is the maximum degree in the graph. The MIS problem in fully dynamic graphs has attracted significant attention after a breakthrough result of Assadi, Onak, Schieber, and Solomon [STOC'18] who presented an algorithm with O(m^3/4) update-time (and thus broke the natural Ω(m) barrier) where m denotes the number of edges in the graph. This result was improved in a series of subsequent papers, though, the update-time remained polynomial. In particular, the fastest algorithm prior to our work had O (min{√n, m^1/3}) update-time [Assadi et al. SODA'19]. Our algorithm maintains the lexicographically first MIS over a random order of the vertices. As a result, the same algorithm also maintains a 3-approximation of correlation clustering. We also show that a simpler variant of our algorithm can be used to maintain a random-order lexicographically first maximal matching in the same update-time.

Fully Dynamic Maximal Independent Set with Polylogarithmic Update Time

Graph problems are troublesome when it comes to MapReduce. Typically, to be able to design algorithms that make use of the advantages of MapReduce, assumptions beyond what the model imposes, such as the {\em density} of the input graph, are required. 
In a recent shift, a simple and robust model of MapReduce for graph problems, where the space per machine is set to be $O(|V|)$ has attracted considerable attention. We term this model {\em semi-MapReduce}, or in short, semi-MPC, and focus on its computational power. 
In this short note, we show through a set of simulation methods that semi-MPC is, perhaps surprisingly, almost equivalent to the congested clique model of distributed computing. However, semi-MPC, in addition to round complexity, incorporates another practically important dimension to optimize: the number of machines. Furthermore, we show that algorithms in other distributed computing models, such as CONGEST, can be simulated to run in the same number of rounds of semiMPC while also using an optimal number of machines. We later show the implications of these simulation methods by obtaining improved algorithms for these models using the recent algorithms that have been developed.

Brief Announcement: Semi-MapReduce Meets Congested Clique.

In the Colonel Blotto game, which was initially introduced by Borel in 1921, two colonels simultaneously distribute their troops across different battlefields. The winner of each battlefield is determined independently by a winner-take-all rule. The ultimate payoff of each colonel is the number of battlefields he wins. This game is commonly used for analyzing a wide range of applications such as the U.S presidential election, innovative technology competitions, advertisements, etc. There have been persistent efforts for finding the optimal strategies for the Colonel Blotto game. After almost a century Ahmadinejad, Dehghani, Hajiaghayi, Lucier, Mahini, and Seddighin provided a poly-time algorithm for finding the optimal strategies. They first model the problem by a Linear Program (LP) and use Ellipsoid method to solve it. However, despite the theoretical importance of their algorithm, it is highly impractical. In general, even Simplex method (despite its exponential running-time) performs better than Ellipsoid method in practice. In this paper, we provide the first polynomial-size LP formulation of the optimal strategies for the Colonel Blotto game. We use linear extension techniques. Roughly speaking, we project the strategy space polytope to a higher dimensional space, which results in a lower number of facets for the polytope. We use this polynomial-size LP to provide a novel, simpler and significantly faster algorithm for finding the optimal strategies for the Colonel Blotto game. We further show this representation is asymptotically tight in terms of the number of constraints. We also extend our approach to multi-dimensional Colonel Blotto games, and implement our algorithm to observe interesting properties of Colonel Blotto; for example, we observe the behavior of players in the discrete model is very similar to the previously studied continuous model.

Mahsa Derakhshan

Papers

Affinity Clustering: Hierarchical Clustering at Scale

Massively Parallel Computation of Matching and MIS in Sparse Graphs

Fully Dynamic Maximal Independent Set with Polylogarithmic Update Time

Brief Announcement: Semi-MapReduce Meets Congested Clique.

Faster and Simpler Algorithm for Optimal Strategies of Blotto Game