207 research outputs found
Ranking with Submodular Valuations
We study the problem of ranking with submodular valuations. An instance of
this problem consists of a ground set , and a collection of monotone
submodular set functions , where each .
An additional ingredient of the input is a weight vector . The
objective is to find a linear ordering of the ground set elements that
minimizes the weighted cover time of the functions. The cover time of a
function is the minimal number of elements in the prefix of the linear ordering
that form a set whose corresponding function value is greater than a unit
threshold value.
Our main contribution is an -approximation algorithm
for the problem, where is the smallest non-zero marginal value that
any function may gain from some element. Our algorithm orders the elements
using an adaptive residual updates scheme, which may be of independent
interest. We also prove that the problem is -hard to
approximate, unless P = NP. This implies that the outcome of our algorithm is
optimal up to constant factors.Comment: 16 pages, 3 figure
Community-aware network sparsification
Network sparsification aims to reduce the number of edges of a network while maintaining its structural properties; such properties include shortest paths, cuts, spectral measures, or network modularity. Sparsification has multiple applications, such as, speeding up graph-mining algorithms, graph visualization, as well as identifying the important network edges.
In this paper we consider a novel formulation of the network-sparsification problem. In addition to the network, we also consider as input a set of communities. The goal is to sparsify the network so as to preserve the network structure with respect to the given communities. We introduce two variants of the community-aware sparsification problem, leading to sparsifiers that satisfy different connectedness community properties. From the technical point of view, we prove hardness results and devise effective approximation algorithms. Our experimental results on a large collection of datasets demonstrate the effectiveness of our algorithms.https://epubs.siam.org/doi/10.1137/1.9781611974973.48Accepted manuscrip
Traffic-Redundancy Aware Network Design
We consider network design problems for information networks where routers
can replicate data but cannot alter it. This functionality allows the network
to eliminate data-redundancy in traffic, thereby saving on routing costs. We
consider two problems within this framework and design approximation
algorithms.
The first problem we study is the traffic-redundancy aware network design
(RAND) problem. We are given a weighted graph over a single server and many
clients. The server owns a number of different data packets and each client
desires a subset of the packets; the client demand sets form a laminar set
system. Our goal is to connect every client to the source via a single path,
such that the collective cost of the resulting network is minimized. Here the
transportation cost over an edge is its weight times times the number of
distinct packets that it carries.
The second problem is a facility location problem that we call RAFL. Here the
goal is to find an assignment from clients to facilities such that the total
cost of routing packets from the facilities to clients (along unshared paths),
plus the total cost of "producing" one copy of each desired packet at each
facility is minimized.
We present a constant factor approximation for the RAFL and an O(log P)
approximation for RAND, where P is the total number of distinct packets. We
remark that P is always at most the number of different demand sets desired or
the number of clients, and is generally much smaller.Comment: 17 pages. To be published in the proceedings of the Twenty-Third
Annual ACM-SIAM Symposium on Discrete Algorithm
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