5,191 research outputs found
Sketch-based Influence Maximization and Computation: Scaling up with Guarantees
Propagation of contagion through networks is a fundamental process. It is
used to model the spread of information, influence, or a viral infection.
Diffusion patterns can be specified by a probabilistic model, such as
Independent Cascade (IC), or captured by a set of representative traces.
Basic computational problems in the study of diffusion are influence queries
(determining the potency of a specified seed set of nodes) and Influence
Maximization (identifying the most influential seed set of a given size).
Answering each influence query involves many edge traversals, and does not
scale when there are many queries on very large graphs. The gold standard for
Influence Maximization is the greedy algorithm, which iteratively adds to the
seed set a node maximizing the marginal gain in influence. Greedy has a
guaranteed approximation ratio of at least (1-1/e) and actually produces a
sequence of nodes, with each prefix having approximation guarantee with respect
to the same-size optimum. Since Greedy does not scale well beyond a few million
edges, for larger inputs one must currently use either heuristics or
alternative algorithms designed for a pre-specified small seed set size.
We develop a novel sketch-based design for influence computation. Our greedy
Sketch-based Influence Maximization (SKIM) algorithm scales to graphs with
billions of edges, with one to two orders of magnitude speedup over the best
greedy methods. It still has a guaranteed approximation ratio, and in practice
its quality nearly matches that of exact greedy. We also present influence
oracles, which use linear-time preprocessing to generate a small sketch for
each node, allowing the influence of any seed set to be quickly answered from
the sketches of its nodes.Comment: 10 pages, 5 figures. Appeared at the 23rd Conference on Information
and Knowledge Management (CIKM 2014) in Shanghai, Chin
Seeding with Costly Network Information
We study the task of selecting nodes in a social network of size , to
seed a diffusion with maximum expected spread size, under the independent
cascade model with cascade probability . Most of the previous work on this
problem (known as influence maximization) focuses on efficient algorithms to
approximate the optimal seed set with provable guarantees, given the knowledge
of the entire network. However, in practice, obtaining full knowledge of the
network is very costly. To address this gap, we first study the achievable
guarantees using influence samples. We provide an approximation
algorithm with a tight (1-1/e){\mbox{OPT}}-\epsilon n guarantee, using
influence samples and show that this dependence on
is asymptotically optimal. We then propose a probing algorithm that queries
edges from the graph and use them to find a seed set with the
same almost tight approximation guarantee. We also provide a matching (up to
logarithmic factors) lower-bound on the required number of edges. To address
the dependence of our probing algorithm on the independent cascade probability
, we show that it is impossible to maintain the same approximation
guarantees by controlling the discrepancy between the probing and seeding
cascade probabilities. Instead, we propose to down-sample the probed edges to
match the seeding cascade probability, provided that it does not exceed that of
probing. Finally, we test our algorithms on real world data to quantify the
trade-off between the cost of obtaining more refined network information and
the benefit of the added information for guiding improved seeding strategies
Importance Sketching of Influence Dynamics in Billion-scale Networks
The blooming availability of traces for social, biological, and communication
networks opens up unprecedented opportunities in analyzing diffusion processes
in networks. However, the sheer sizes of the nowadays networks raise serious
challenges in computational efficiency and scalability.
In this paper, we propose a new hyper-graph sketching framework for inflence
dynamics in networks. The central of our sketching framework, called SKIS, is
an efficient importance sampling algorithm that returns only non-singular
reverse cascades in the network. Comparing to previously developed sketches
like RIS and SKIM, our sketch significantly enhances estimation quality while
substantially reducing processing time and memory-footprint. Further, we
present general strategies of using SKIS to enhance existing algorithms for
influence estimation and influence maximization which are motivated by
practical applications like viral marketing. Using SKIS, we design high-quality
influence oracle for seed sets with average estimation error up to 10x times
smaller than those using RIS and 6x times smaller than SKIM. In addition, our
influence maximization using SKIS substantially improves the quality of
solutions for greedy algorithms. It achieves up to 10x times speed-up and 4x
memory reduction for the fastest RIS-based DSSA algorithm, while maintaining
the same theoretical guarantees.Comment: 12 pages, to appear in ICDM 2017 as a regular pape
The Solution Distribution of Influence Maximization: A High-level Experimental Study on Three Algorithmic Approaches
Influence maximization is among the most fundamental algorithmic problems in
social influence analysis. Over the last decade, a great effort has been
devoted to developing efficient algorithms for influence maximization, so that
identifying the ``best'' algorithm has become a demanding task. In SIGMOD'17,
Arora, Galhotra, and Ranu reported benchmark results on eleven existing
algorithms and demonstrated that there is no single state-of-the-art offering
the best trade-off between computational efficiency and solution quality.
In this paper, we report a high-level experimental study on three
well-established algorithmic approaches for influence maximization, referred to
as Oneshot, Snapshot, and Reverse Influence Sampling (RIS). Different from
Arora et al., our experimental methodology is so designed that we examine the
distribution of random solutions, characterize the relation between the sample
number and the actual solution quality, and avoid implementation dependencies.
Our main findings are as follows: 1. For a sufficiently large sample number, we
obtain a unique solution regardless of algorithms. 2. The average solution
quality of Oneshot, Snapshot, and RIS improves at the same rate up to scaling
of sample number. 3. Oneshot requires more samples than Snapshot, and Snapshot
requires fewer but larger samples than RIS. We discuss the time efficiency when
conditioning Oneshot, Snapshot, and RIS to be of identical accuracy. Our
conclusion is that Oneshot is suitable only if the size of available memory is
limited, and RIS is more efficient than Snapshot for large networks; Snapshot
is preferable for small, low-probability networks.Comment: To appear in SIGMOD 202
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