1 research outputs found
The Undirected Optical Indices of Complete -ary Trees
The routing and wavelength assignment problem arises from the investigation
of optimal wavelength allocation in an optical network that employs Wavelength
Division Multiplexing (WDM). Consider an optical network that is represented by
a connected, simple graph . An all-to-all routing in is a set of
paths connecting all pairs of vertices of . The undirected optical index of
is the minimum integer to guarantee the existence of a mapping
, such that if and
have common edge(s), over all possible routings . A natural lower bound of
the undirected optical index of is the (undirected) edge-forwarding index,
which is defined to be the minimum of the maximum edge-load over all possible
all-to-all routings. In this paper, we first derive the exact value of the
optical index of the complete -ary trees, and then investigate the gap
between undirected optical and edge-forwarding indices.Comment: 12 pages, 3 figure