Efficient Probabilistic K-Core Computation on Uncertain Graphs

Abstract

As uncertainty is inherent in a wide spectrum of graph applications such as social network and brain network, it is highly demanded to re-visit classical graph problems in the context of uncertain graphs. Driven by real-applications, in this paper, we study the problem of k-core computation on uncertain graphs and propose a new model, namely (,)-core, which consists of nodes with probability at least to be kcore member in the uncertain graph. We show the computation of (,)-core is NP-hard, and hence resort to sampling based methods. Effective and efficient pruning techniques are proposed to significantly reduce the candidate size. To further reduce the cost of k-core computation on multiple sampled graphs, we design a k-core membership check algorithm following a novel expansion-based search paradigm. Extensive experiments on reallife graphs demonstrate the effectiveness and efficiency of our proposed techniques.

Finding Route Hotspots in Large Labeled Networks

“…On one hand, various community models have been proposed to describe dense subgraphs, such as k-core [6] and k-truss [7]. But these dense subgraphs cannot be adopted to model route hotspots as they mainly focus on the graph structures but ignore how routes perform.…”

“…The colored arrow lines on edges represent routes, where a route T is a sequence of consecutive edges. The dashed ellipse represents a route hotspot (i.e., the induced subgraph H of {v 4 , v 6 , v 7 , v 9 }) that can be marked by the sequential pattern P S, M S, DB , which is covered by qualified routes that form this hotspot. consecutive collaborative authors A and B in the route, B should have cited a paper published by A.…”

Efficient algorithms for densest subgraph discovery

“…Other Dense Subgraphs. Recently, many other dense subgraph models [24], such as k-core [7,47,51,23,22,20,25,26,67,12], k-truss [15,37,69,39,38], k-(r, s) nucleus [60,58,61,59] (a generalization of k-core and k-truss), k-clique [16,34], k-edge connected components [35,36]. and k-plexes [63], have also been explored.…”

Parameterized Optimization in Uncertain Graphs—A Survey and Some Results

“…an indicator function that takes value one if and only if there is a d-core of H that contains v, and P(H) is probability of the possible world H. In this setting, we consider the (d, θ)-core problem defined by Peng et al [16]. We refer to this problem as the INDIVIDUAL CORE problem and it is defined as follows.…”

“…A natural question is there are problems which have efficient algorithms on a graph in which the edges have no uncertainty but become hard on uncertain graphs. The typical optimization problems considered on uncertain graphs are shortest path [5], reliability [6], minimum spanning trees [7,8], maxflows [9,10], maximum coverage [11][12][13], influence maximization [14] and densest subgraph [15,16]. This article is structured partly as a survey and partly as an original research article.…”