1,856 research outputs found
Building Damage-Resilient Dominating Sets in Complex Networks against Random and Targeted Attacks
We study the vulnerability of dominating sets against random and targeted
node removals in complex networks. While small, cost-efficient dominating sets
play a significant role in controllability and observability of these networks,
a fixed and intact network structure is always implicitly assumed. We find that
cost-efficiency of dominating sets optimized for small size alone comes at a
price of being vulnerable to damage; domination in the remaining network can be
severely disrupted, even if a small fraction of dominator nodes are lost. We
develop two new methods for finding flexible dominating sets, allowing either
adjustable overall resilience, or dominating set size, while maximizing the
dominated fraction of the remaining network after the attack. We analyze the
efficiency of each method on synthetic scale-free networks, as well as real
complex networks
Adding Isolated Vertices Makes some Online Algorithms Optimal
An unexpected difference between online and offline algorithms is observed.
The natural greedy algorithms are shown to be worst case online optimal for
Online Independent Set and Online Vertex Cover on graphs with 'enough' isolated
vertices, Freckle Graphs. For Online Dominating Set, the greedy algorithm is
shown to be worst case online optimal on graphs with at least one isolated
vertex. These algorithms are not online optimal in general. The online
optimality results for these greedy algorithms imply optimality according to
various worst case performance measures, such as the competitive ratio. It is
also shown that, despite this worst case optimality, there are Freckle graphs
where the greedy independent set algorithm is objectively less good than
another algorithm. It is shown that it is NP-hard to determine any of the
following for a given graph: the online independence number, the online vertex
cover number, and the online domination number.Comment: A footnote in the .tex file didn't show up in the last version. This
was fixe
Approximation Algorithms for the Capacitated Domination Problem
We consider the {\em Capacitated Domination} problem, which models a
service-requirement assignment scenario and is also a generalization of the
well-known {\em Dominating Set} problem. In this problem, given a graph with
three parameters defined on each vertex, namely cost, capacity, and demand, we
want to find an assignment of demands to vertices of least cost such that the
demand of each vertex is satisfied subject to the capacity constraint of each
vertex providing the service. In terms of polynomial time approximations, we
present logarithmic approximation algorithms with respect to different demand
assignment models for this problem on general graphs, which also establishes
the corresponding approximation results to the well-known approximations of the
traditional {\em Dominating Set} problem. Together with our previous work, this
closes the problem of generally approximating the optimal solution. On the
other hand, from the perspective of parameterization, we prove that this
problem is {\it W[1]}-hard when parameterized by a structure of the graph
called treewidth. Based on this hardness result, we present exact
fixed-parameter tractable algorithms when parameterized by treewidth and
maximum capacity of the vertices. This algorithm is further extended to obtain
pseudo-polynomial time approximation schemes for planar graphs
Multiple domination models for placement of electric vehicle charging stations in road networks
Electric and hybrid vehicles play an increasing role in the road transport
networks. Despite their advantages, they have a relatively limited cruising
range in comparison to traditional diesel/petrol vehicles, and require
significant battery charging time. We propose to model the facility location
problem of the placement of charging stations in road networks as a multiple
domination problem on reachability graphs. This model takes into consideration
natural assumptions such as a threshold for remaining battery load, and
provides some minimal choice for a travel direction to recharge the battery.
Experimental evaluation and simulations for the proposed facility location
model are presented in the case of real road networks corresponding to the
cities of Boston and Dublin.Comment: 20 pages, 5 figures; Original version from March-April 201
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