Abstract
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.
Highlights
We study the vulnerability of dominating sets against random and targeted node removals in complex networks
We start our analysis by measuring the stability of three different dominating sets, that we use for baseline comparison with our new methods
Greedy minimum dominating set (MDS)[1,4,31], where nodes are selected by a sequential greedy search algorithm in order to approximate the actual (NP-hard) smallest dominating set
Summary
We study the vulnerability of dominating sets against random and targeted node removals in complex networks. The connectivity of the surviving network structures and the fraction of the remaining set of nodes still dominated following failures or attacks are both essential for sustainable network operations and carrying out network functions. While the former (structural integrity) has been studied in great detail over the past two decades[19,20,21,22,23,24,25], the latter (domination stability) has not received any attention
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