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The Random Walk with d Choice RWC(d ) is a recently proposed variation of the simple Random Walk
that first selects a subset of d neighbor nodes and then decides to move to the node which minimizes the
value of a certain parameter; this parameter captures the number of past visits of the walk to that node. In
this paper, we propose the Enhanced Random Walk with d Choice algorithm ERWC(d, h) which first
selects a subset of d neighbor nodes and then decides to move to the node which minimizes a value H
defined at every node; this H value depends on a parameter h and captures information about past visits
of the walk to that node and  with a certain weight  to its neighbors. Simulations of the Enhanced Random
Walk with d Choice algorithm on various types of graphs indicate beneficial results with respect to Cover
Time and Load Balancing. The graph types used are the Random Geometric Graph, Torus, Grid,
Hypercube, Lollipop and Bernoulli.
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