skip to main content
US FlagAn official website of the United States government
dot gov icon
Official websites use .gov
A .gov website belongs to an official government organization in the United States.
https lock icon
Secure .gov websites use HTTPS
A lock ( lock ) or https:// means you've safely connected to the .gov website. Share sensitive information only on official, secure websites.

Explore Research Products in the PAR
It may take a few hours for recently added research products to appear in PAR search results.


Title: Current Flow Group Closeness Centrality for Complex Networks?
Current flow closeness centrality (CFCC) has a better discriminating ability than the ordinary closeness centrality based on shortest paths. In this paper, we extend this notion to a group of vertices in a weighted graph, and then study the problem of finding a subset S of k vertices to maximize its CFCC C(S), both theoretically and experimentally. We show that the problem is NP-hard, but propose two greedy algorithms for minimizing the reciprocal of C(S) with provable guarantees using the monotoncity and supermodularity. The first is a deterministic algorithm with an approximation factor (1−kk−1⋅1e) and cubic running time; while the second is a randomized algorithm with a (1−kk−1⋅1e−ϵ)-approximation and nearly-linear running time for any ϵ>0. Extensive experiments on model and real networks demonstrate that our algorithms are effective and efficient, with the second algorithm being scalable to massive networks with more than a million vertices.  more » « less
Award ID(s):
1637566
PAR ID:
10113894
Author(s) / Creator(s):
; ; ; ;
Date Published:
Journal Name:
The World Wide Web Conference, WWW 2019, San Francisco, CA, USA, May 13-17, 2019
Page Range / eLocation ID:
961 to 971
Format(s):
Medium: X
Sponsoring Org:
National Science Foundation
More Like this
  1. ; ; ; ; (, Schloss Dagstuhl – Leibniz-Zentrum für Informatik)
    Leroux, Jérôme; Lombardy, Sylvain; Peleg, David (Ed.)
    Feedback Vertex Set (FVS) is one of the most studied vertex deletion problems in the field of graph algorithms. In the decision version of the problem, given a graph G and an integer k, the question is whether there exists a set S of at most k vertices in G such that G-S is acyclic. It is one of the first few problems which were shown to be NP-complete, and has been extensively studied from the viewpoint of approximation and parameterized algorithms. The best-known polynomial time approximation algorithm for FVS is a 2-factor approximation, while the best known deterministic and randomized FPT algorithms run in time 𝒪^*(3.460^k) and 𝒪^*(2.7^k) respectively. In this paper, we contribute to the newly established area of parameterized approximation, by studying FVS in this paradigm. In particular, we combine the approaches of parameterized and approximation algorithms for the study of FVS, and achieve an approximation guarantee with a factor better than 2 in randomized FPT running time, that improves over the best known parameterized algorithm for FVS. We give three simple randomized (1+ε) approximation algorithms for FVS, running in times 𝒪^*(2^{εk}⋅ 2.7^{(1-ε)k}), 𝒪^*(({(4/(1+ε))^{(1+ε)}}⋅{(ε/3)^ε})^k), and 𝒪^*(4^{(1-ε)k}) respectively for every ε ∈ (0,1). Combining these three algorithms, we obtain a factor (1+ε) approximation algorithm for FVS, which has better running time than the best-known (randomized) FPT algorithm for every ε ∈ (0, 1). This is the first attempt to look at a parameterized approximation of FVS to the best of our knowledge. Our algorithms are very simple, and they rely on some well-known reduction rules used for arriving at FPT algorithms for FVS. 
    more » « less
  2. ; ; ; (, The 2016 IEEE/ACM International Conference on Advances in Social Networks Analysis and Mining)
    In this paper we evaluate the effect of noise on community scoring and centrality-based parameters with respect to two different aspects of network analysis: (i) sensitivity, that is how the parameter value changes as edges are removed and (ii) reliability in the context of message spreading, that is how the time taken to broadcast a message changes as edges are removed. Our experiments on synthetic and real-world networks and three different noise models demonstrate that for both the aspects over all networks and all noise models, permanence qualifies as the most effective metric. For the sensitivity experiments closeness centrality is a close second. For the message spreading experiments, closeness and betweenness centrality based initiator selection closely competes with permanence. This is because permanence has a dual characteristic where the cumulative permanence over all vertices is sensitive to noise but the ids of the top-rank vertices, which are used to find seeds during message spreading remain relatively stable under noise. 
    more » « less
  3. ; ; ; ; ; (, Arxiv)
    We develop a general framework, called approximately-diverse dynamic programming (ADDP) that can be used to generate a collection of k≥2 maximally diverse solutions to various geometric and combinatorial optimization problems. Given an approximation factor 0≤c≤1, this framework also allows for maximizing diversity in the larger space of c-approximate solutions. We focus on two geometric problems to showcase this technique: 1. Given a polygon P, an integer k≥2 and a value c≤1, generate k maximally diverse c-nice triangulations of P. Here, a c-nice triangulation is one that is c-approximately optimal with respect to a given quality measure σ. 2. Given a planar graph G, an integer k≥2 and a value c≤1, generate k maximally diverse c-optimal Independent Sets (or, Vertex Covers). Here, an independent set S is said to be c-optimal if |S|≥c|S′| for any independent set S′ of G. Given a set of k solutions to the above problems, the diversity measure we focus on is the average distance between the solutions, where d(X,Y)=|XΔY|. For arbitrary polygons and a wide range of quality measures, we give poly(n,k) time (1−Θ(1/k))-approximation algorithms for the diverse triangulation problem. For the diverse independent set and vertex cover problems on planar graphs, we give an algorithm that runs in time 2^(O(k.δ^(−1).ϵ^(−2)).n^O(1/ϵ) and returns (1−ϵ)-approximately diverse (1−δ)c-optimal independent sets or vertex covers. Our triangulation results are the first algorithmic results on computing collections of diverse geometric objects, and our planar graph results are the first PTAS for the diverse versions of any NP-complete problem. Additionally, we also provide applications of this technique to diverse variants of other geometric problems. 
    more » « less
  4. ; (, SIAM 2020 Workshop on Combinatorial Scientific Computing)
    We consider the maximum vertex-weighted matching problem (MVM), in which non-negative weights are assigned to the vertices of a graph, and the weight of a matching is the sum of the weights of the matched vertices. Although exact algorithms for MVM are faster than exact algorithms for the maximum edge-weighted matching problem, there are graphs on which these exact algorithms could take hundreds of hours. For a natural number k, we design a k/(k + 1)approximation algorithm for MVM on non-bipartite graphs that updates the matching along certain short paths in the graph: either augmenting paths of length at most 2k + 1 or weight-increasing paths of length at most 2k. The choice of k = 2 leads to a 2/3-approximation algorithm that computes nearly optimal weights fast. This algorithm could be initialized with a 2/3-approximate maximum cardinality matching to reduce its runtime in practice. A 1/2-approximation algorithm may be obtained using k = 1, which is faster than the 2/3-approximation algorithm but it computes lower weights. The 2/3-approximation algorithm has time complexity O(Δ2m) while the time complexity of the 1/2-approximation algorithm is O(Δm), where m is the number of edges and Δ is the maximum degree of a vertex. Results from our serial implementations show that on average the 1/2-approximation algorithm runs faster than the Suitor algorithm (currently the fastest 1/2-approximation algorithm) while the 2/3-approximation algorithm runs as fast as the Suitor algorithm but obtains higher weights for the matching. One advantage of the proposed algorithms is that they are well-suited for parallel implementation since they can process vertices to match in any order. The 1/2- and 2/3-approximation algorithms have been implemented on a shared memory parallel computer, and both approximation algorithms obtain good speedups, while the former algorithm runs faster on average than the parallel Suitor algorithm. Care is needed to design the parallel algorithm to avoid cyclic waits, and we prove that it is live-lock free. 
    more » « less
  5. ; (, Mathematics of Operations Research)
    We consider the following general network design problem. The input is an asymmetric metric (V, c), root [Formula: see text], monotone submodular function [Formula: see text], and budget B. The goal is to find an r-rooted arborescence T of cost at most B that maximizes f(T). Our main result is a simple quasi-polynomial time [Formula: see text]-approximation algorithm for this problem, in which [Formula: see text] is the number of vertices in an optimal solution. As a consequence, we obtain an [Formula: see text]-approximation algorithm for directed (polymatroid) Steiner tree in quasi-polynomial time. We also extend our main result to a setting with additional length bounds at vertices, which leads to improved [Formula: see text]-approximation algorithms for the single-source buy-at-bulk and priority Steiner tree problems. For the usual directed Steiner tree problem, our result matches the best previous approximation ratio but improves significantly on the running time. For polymatroid Steiner tree and single-source buy-at-bulk, our result improves prior approximation ratios by a logarithmic factor. For directed priority Steiner tree, our result seems to be the first nontrivial approximation ratio. Under certain complexity assumptions, our approximation ratios are the best possible (up to constant factors). 
    more » « less
  • Citation Formats
  • MLA
  • APA
  • Chicago
  • BibTeX
  • Save / Share this Record
  • Send to Email