Zihan Tan

Hsien-Chih Chang, Jonathan Conroy, Zihan Tan et al.

In this paper we construct distance sketches for intersection graphs of arbitrary path-connected regions in the plane (known as the string graphs) in the constant and $1+\varepsilon$ distortion regimes. Furthermore, the distance sketches themselves are planar graphs. First, we show that every unweighted string graph $G$ has an $O(1)$-distortion planar emulator: that is, there exists an edge-weighted planar graph $H$ containing every vertex in $G$, such that every pair of vertices $(u,v)$ satisfies $δ_G(u,v) \le δ_H(u,v) \le O(1) \cdot δ_G(u,v)$. Furthermore, we show that for any constant $\varepsilon > 0$, there is an edge-weighted planar graph $H'$ such that every pair of vertices $(u,v)$ satisfies $δ_G(u,v) \le δ_{H'}(u,v) \le (1+\varepsilon) \cdot δ_G(u,v) + O(\varepsilon^{-4}\textrm{poly}\log n)$. No previous constructions of sparse distance sketches were known even for intersection graphs of simple shapes like axis-parallel rectangles or fat convex polygons. As applications, we construct the first $(1+\varepsilon, +O(1))$ mixed-distortion tree cover and distance oracle for arbitrary string graphs, as well as the first additive $+(\varepsilonΔ+O(1))$-distortion embedding of string graphs $G$ with diameter $Δ$ into graphs of constant treewidth $O(\varepsilon^{-4})$.

Yu Chen, Zihan Tan

We study the following distance realization problem: given a metric $D$ on a set $T$ of terminals, does there exist an (edge-weighted) outerplanar graph $G$, such that $T\subseteq V(G)$, and for every pair $t,t'\in T$, $\textsf{dist}_G(t,t')=D(t,t')$? We first prove that there is no ``local characterization'', forming a contrast with trees and Okamura-Seymour instances. Our main result is an efficient algorithm for this problem whose running time is polynomial in $|T|$. Both our proof and our algorithm utilize a recent new approach of analyzing graph structures, by viewing graphs as paths and their intersections, which we believe is of independent interest.

Wei Chen, Tian Lin, Zihan Tan et al.

In this paper, we address the important issue of uncertainty in the edge influence probability estimates for the well studied influence maximization problem --- the task of finding $k$ seed nodes in a social network to maximize the influence spread. We propose the problem of robust influence maximization, which maximizes the worst-case ratio between the influence spread of the chosen seed set and the optimal seed set, given the uncertainty of the parameter input. We design an algorithm that solves this problem with a solution-dependent bound. We further study uniform sampling and adaptive sampling methods to effectively reduce the uncertainty on parameters and improve the robustness of the influence maximization task. Our empirical results show that parameter uncertainty may greatly affect influence maximization performance and prior studies that learned influence probabilities could lead to poor performance in robust influence maximization due to relatively large uncertainty in parameter estimates, and information cascade based adaptive sampling method may be an effective way to improve the robustness of influence maximization.