arXiv subjects

J. David Smith

Publications and source records attributed to J. David Smith.

4 recordsLinked to original sources

arXiv2019

TipTop: (Almost) Exact Solutions for Influence Maximization in Billion-scale Networks

In this paper, we study the Cost-aware Target Viral Marketing (CTVM) problem, a generalization of Influence Maximization (IM). CTVM asks for the most cost-effective users to influence the most relevant users. In contrast to the vast literature, we attempt to offer exact solutions. As the problem is NP-hard, thus, exact solutions are intractable, we propose TipTop, a $(1-ε)$-optimal solution for arbitrary $ε>0$ that scales to very large networks such as Twitter. At the heart of TipTop lies an innovative technique that reduces the number of samples as much as possible. This allows us to exactly solve CTVM on a much smaller space of generated samples using Integer Programming. Furthermore, TipTop lends a tool for researchers to benchmark their solutions against the optimal one in large-scale networks, which is currently not available.

cs.SI↗

arXiv2018

Fast Maximization of Non-Submodular, Monotonic Functions on the Integer Lattice

The optimization of submodular functions on the integer lattice has received much attention recently, but the objective functions of many applications are non-submodular. We provide two approximation algorithms for maximizing a non-submodular function on the integer lattice subject to a cardinality constraint; these are the first algorithms for this purpose that have polynomial query complexity. We propose a general framework for influence maximization on the integer lattice that generalizes prior works on this topic, and we demonstrate the efficiency of our algorithms in this context.

cs.DS↗

arXiv2018

Deterministic & Adaptive Non-Submodular Maximization via the Primal Curvature

While greedy algorithms have long been observed to perform well on a wide variety of problems, up to now approximation ratios have only been known for their application to problems having submodular objective functions $f$. Since many practical problems have non-submodular $f$, there is a critical need to devise new techniques to bound the performance of greedy algorithms in the case of non-submodularity. Our primary contribution is the introduction of a novel technique for estimating the approximation ratio of the greedy algorithm for maximization of monotone non-decreasing functions based on the curvature of $f$ without relying on the submodularity constraint. We show that this technique reduces to the classical $(1 - 1/e)$ ratio for submodular functions. Furthermore, we develop an extension of this ratio to the adaptive greedy algorithm, which allows applications to non-submodular stochastic maximization problems. This notably extends support to applications modeling incomplete data with uncertainty.

cs.DS↗

arXiv2012

Hovering UFO Droplets

This fluid dynamics video is an entry for the Gallery of Fluid Motion of the 65th Annual Meeting of the APS-DFD. This video shows behavior of condensing droplets on a lubricant impregnated surface and a comparison with a superhydrophobic surface. On impregnated surfaces, drops appear like UFOs hovering over a surface. The videos were recorded in an Environmental SEM and a specially built condensation rig.

physics.flu-dyn↗