Computational geometry

Influence Maximization (IM), which selects a set of $k$ users (called seed set) from a social network to maximize the expected number of influenced users (called influence spread), is a key algorithmic problem in social influence analysis. Due to its immense application potential and enormous technical challenges, IM has been extensively studied in the past decade. In this paper, we survey and synthesize a wide spectrum of existing studies on IM from an algorithmic perspective , with a special focus on the following key aspects: (1) a review of well-accepted diffusion models that capture the information diffusion process and build the foundation of the IM problem, (2) a fine-grained taxonomy to classify existing IM algorithms based on their design objectives, (3) a rigorous theoretical comparison of existing IM algorithms, and (4) a comprehensive study on the applications of IM techniques in combining with novel context features of social networks such as topic, location, and time. Based on this analysis, we then outline the key challenges and research directions to expand the boundary of IM research.

https://ink.library.smu.edu.sg/cgi/viewcontent.cgi?article=4983&context=sis_research

Influence Maximization on Social Graphs: A Survey

Network embedding, which aims to learn the lowdimensional representations of vertices, is an important task and has attracted considerable research efforts recently. In real world, networks, like social network and biological networks, are dynamic and evolving over time. However, almost all the existing network embedding methods focus on static networks while ignore network dynamics. In this paper, we present a novel representation learning approach, DynamicTriad, to preserve both structural information and evolution patterns of a given network. The general idea of our approach is to impose triad, which is a group of three vertices and is one of the basic units of networks. In particular, we model how a closed triad, which consists of three vertices connected with each other, develops from an open triad that has two of three vertices not connected with each other. This triadic closure process is a fundamental mechanism in the formation and evolution of networks, thereby makes our model being able to capture the network dynamics and to learn representation vectors for each vertex at different time steps. Experimental results on three real-world networks demonstrate that, compared with several state-of-the-art techniques, DynamicTriad achieves substantial gains in several application scenarios. For example, our approach can effectively be applied and help to identify telephone frauds in a mobile network, and to predict whether a user will repay her loans or not in a loan network.

Dynamic Network Embedding by Modeling Triadic Closure Process.

One of the main challenges that the Semantic Web faces is the integration of a growing number of independently designed ontologies. In this work, we present PARIS, an approach for the automatic alignment of ontologies. PARIS aligns not only instances, but also relations and classes. Alignments at the instance level cross-fertilize with alignments at the schema level. Thereby, our system provides a truly holistic solution to the problem of ontology alignment. The heart of the approach is probabilistic, i.e., we measure degrees of matchings based on probability estimates. This allows PARIS to run without any parameter tuning. We demonstrate the efficiency of the algorithm and its precision through extensive experiments. In particular, we obtain a precision of around 90% in experiments with some of the world's largest ontologies.

PARIS: Probabilistic Alignment of Relations, Instances, and Schema

Motivation Network alignment aims to find conserved regions between different networks. Existing methods aim to maximize total similarity over all aligned nodes (i.e. node conservation). Then, they evaluate alignment quality by measuring the amount of conserved edges, but only after the alignment is constructed. Thus, we recently introduced MAGNA (Maximizing Accuracy in Global Network Alignment) to directly maximize edge conservation while producing alignments and showed its superiority over the existing methods. Here, we extend the original MAGNA with several important algorithmic advances into a new MAGNA++ framework. Results MAGNA++ introduces several novelties: (i) it simultaneously maximizes any one of three different measures of edge conservation (including our recent superior [Formula: see text] measure) and any desired node conservation measure, which further improves alignment quality compared with maximizing only node conservation or only edge conservation; (ii) it speeds up the original MAGNA algorithm by parallelizing it to automatically use all available resources, as well as by reimplementing the edge conservation measures more efficiently; (iii) it provides a friendly graphical user interface for easy use by domain (e.g. biological) scientists; and (iv) at the same time, MAGNA++ offers source code for easy extensibility by computational scientists. Availability and implementation http://www.nd.edu/∼cone/MAGNA++/

MAGNA++: Maximizing Accuracy in Global Network Alignment via both node and edge conservation.

Social influence and influence diffusion has been widely studied in online social networks. However, most existing works on influence diffusion focus on static networks. In this paper, we study the problem of maximizing influence diffusion in a dynamic social network. Specifically, the network changes over time and the changes can be only observed by periodically probing some nodes for the update of their connections. Our goal then is to probe a subset of nodes in a social network so that the actual influence diffusion process in the network can be best uncovered with the probing nodes. We propose a novel algorithm to approximate the optimal solution. The algorithm, through probing a small portion of the network, minimizes the possible error between the observed network and the real network. We evaluate the proposed algorithm on both synthetic and real large networks. Experimental results show that our proposed algorithm achieves a better performance than several alternative algorithms.

/pdf/influence-maximization-in-dynamic-social-networks-1u2q7o0uhc.pdf

Influence Maximization in Dynamic Social Networks

Network alignment can be used to transfer functional knowledge between conserved regions of different networks. Existing methods use a node cost function (NCF) to compare nodes across networks and an alignment strategy (AS) to find high-scoring alignments with respect to total NCF over all aligned nodes (or node conservation). Then, they evaluate alignments via a measure that is different than node conservation used to guide alignment construction. Typically, one measures edge conservation, but only after alignments are produced. Hence, we recently directly maximized edge conservation while constructing alignments, which improved their quality. Here, we aim to maximize both node and edge conservation during alignment construction to further improve quality. We design a novel measure of edge conservation that (unlike existing measures that treat each conserved edge the same) weighs conserved edges to favor edges with highly NCF-similar end-nodes. As a result, we introduce a novel AS, Weighted Alignment VotEr (WAVE), which can optimize any measures of node and edge conservation. Using WAVE on top of well-established NCFs improves alignments compared to existing methods that optimize only node or edge conservation or treat each conserved edge the same. We evaluate WAVE on biological data, but it is applicable in any domain.

https://www.springer.com/cda/content/document/cda_downloaddocument/9783662482209-c2.pdf?SGWID=0-0-45-1524593-p177646782

Simultaneous Optimization of both Node and Edge Conservation in Network Alignment via WAVE

Ordered sets (and maps when data is associated with each key) are one of the most important and useful data types. The set-set functions union, intersection and difference are particularly useful in certain applications. Brown and Tarjan first described an algorithm for these functions, based on 2-3 trees, that meet the optimal Θ(m log (n/m+1)) time bounds in the comparison model (n and m ≤ n are the input sizes). Later Adams showed very elegant algorithms for the functions, and others, based on weight-balanced trees. They only require a single function that is specific to the balancing scheme---a function that joins two balanced trees---and hence can be applied to other balancing schemes. Furthermore the algorithms are naturally parallel. However, in the twenty-four years since, no one has shown that the algorithms, sequential or parallel are asymptotically work optimal. In this paper we show that Adams' algorithms are both work efficient and highly parallel (polylog span) across four different balancing schemes---AVL trees, red-black trees, weight balanced trees and treaps. To do this we use careful, but simple, algorithms for Join that maintain certain invariants, and our proof is (mostly) generic across the schemes.To understand how the algorithms perform in practice we have also implemented them (all code except Join is generic across the balancing schemes). Interestingly the implementations on all four balancing schemes and three set functions perform similarly in time and speedup (more than 45x on 64 cores). We also compare the performance of our implementation to other existing libraries and algorithms.

Just Join for Parallel Ordered Sets

Ordered (key-value) maps are an important and widely-used data type for large-scale data processing frameworks. Beyond simple search, insertion and deletion, more advanced operations such as range extraction, filtering, and bulk updates form a critical part of these frameworks. We describe an interface for ordered maps that is augmented to support fast range queries and sums, and introduce a parallel and concurrent library called PAM (Parallel Augmented Maps) that implements the interface. The interface includes a wide variety of functions on augmented maps ranging from basic insertion and deletion to more interesting functions such as union, intersection, filtering, extracting ranges, splitting, and range-sums. We describe algorithms for these functions that are efficient both in theory and practice. As examples of the use of the interface and the performance of PAM we apply the library to four applications: simple range sums, interval trees, 2D range trees, and ranked word index searching. The interface greatly simplifies the implementation of these data structures over direct implementations. Sequentially the code achieves performance that matches or exceeds existing libraries designed specially for a single application, and in parallel our implementation gets speedups ranging from 40 to 90 on 72 cores with 2-way hyperthreading.

PAM: parallel augmented maps

Semisorting is the problem of reordering an input array of keys such that equal keys are contiguous but different keys are not necessarily in sorted order. Semisorting is important for collecting equal values and is widely used in practice. For example, it is the core of the MapReduce paradigm, is a key component of the database join operation, and has many other applications. We describe a (randomized) parallel algorithm for the problem that is theoretically efficient (linear work and logarithmic depth), but is designed to be more practically efficient than previous algorithms. We use ideas from the parallel integer sorting algorithm of Rajasekaran and Reif, but instead of processing bits of a integers in a reduced range in a bottom-up fashion, we process the hashed values of keys directly top-down. We implement the algorithm and experimentally show on a variety of input distributions that it outperforms a similarly-optimized radix sort on a modern 40-core machine with hyper-threading by about a factor of 1.7--1.9, and achieves a parallel speedup of up to 38x. We discuss the various optimizations used in our implementation and present an extensive experimental analysis of its performance.

/pdf/a-top-down-parallel-semisort-3xcx1ea3ia.pdf

Yihan Sun

Papers

Influence Maximization in Dynamic Social Networks

Simultaneous Optimization of both Node and Edge Conservation in Network Alignment via WAVE

Just Join for Parallel Ordered Sets

PAM: parallel augmented maps

A Top-Down Parallel Semisort