2,707 research outputs found
Forwarding and optical indices of 4-regular circulant networks
An all-to-all routing in a graph is a set of oriented paths of , with
exactly one path for each ordered pair of vertices. The load of an edge under
an all-to-all routing is the number of times it is used (in either
direction) by paths of , and the maximum load of an edge is denoted by
. The edge-forwarding index is the minimum of
over all possible all-to-all routings , and the arc-forwarding index
is defined similarly by taking direction into
consideration, where an arc is an ordered pair of adjacent vertices. Denote by
the minimum number of colours required to colour the paths of such
that any two paths having an edge in common receive distinct colours. The
optical index is defined to be the minimum of over all possible
, and the directed optical index is defined
similarly by requiring that any two paths having an arc in common receive
distinct colours. In this paper we obtain lower and upper bounds on these four
invariants for -regular circulant graphs with connection set , . We give approximation algorithms with performance ratio a
small constant for the corresponding forwarding index and routing and
wavelength assignment problems for some families of -regular circulant
graphs.Comment: 19 pages, no figure in Journal of Discrete Algorithms 201
Setting Parameters by Example
We introduce a class of "inverse parametric optimization" problems, in which
one is given both a parametric optimization problem and a desired optimal
solution; the task is to determine parameter values that lead to the given
solution. We describe algorithms for solving such problems for minimum spanning
trees, shortest paths, and other "optimal subgraph" problems, and discuss
applications in multicast routing, vehicle path planning, resource allocation,
and board game programming.Comment: 13 pages, 3 figures. To be presented at 40th IEEE Symp. Foundations
of Computer Science (FOCS '99
Triple-loop networks with arbitrarily many minimum distance diagrams
Minimum distance diagrams are a way to encode the diameter and routing
information of multi-loop networks. For the widely studied case of double-loop
networks, it is known that each network has at most two such diagrams and that
they have a very definite form "L-shape''.
In contrast, in this paper we show that there are triple-loop networks with
an arbitrarily big number of associated minimum distance diagrams. For doing
this, we build-up on the relations between minimum distance diagrams and
monomial ideals.Comment: 17 pages, 8 figure
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