1 research outputs found
Adaptive Algorithm for Finding Connected Dominating Sets in Uncertain Graphs
The problem of finding a minimum-weight connected dominating set (CDS) of a
given undirected graph has been studied actively, motivated by operations of
wireless ad hoc networks. In this paper, we formulate a new stochastic variant
of the problem. In this problem, each node in the graph has a hidden random
state, which represents whether the node is active or inactive, and we seek a
CDS of the graph that consists of the active nodes. We consider an adaptive
algorithm for this problem, which repeat choosing nodes and observing the
states of the nodes around the chosen nodes until a CDS is found. Our
algorithms have a theoretical performance guarantee that the sum of the weights
of the nodes chosen by the algorithm is at most
times that of any adaptive algorithm in expectation, where is an
approximation factor for the node-weighted polymatroid Steiner tree problem and
is the minimum probability of possible scenarios on the node states.Comment: This is the accepted version of a paper to be published by IEEE/ACM
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