  How many links can be cut before a network is bisected? What is the maximal
bandwidth that can be pushed between two nodes of a network? These questions
are closely related to network resilience, path choice for multipath routing or
bisection bandwidth estimations in data centers. The answer is quantified using
metrics such as the number of edge-disjoint paths between two network nodes and
the cumulative bandwidth that can flow over these paths. In practice though,
such calculations are far from simple due to the restrictive effect of network
policies on path selection. Policies are set by network administrators to
conform to service level agreements, protect valuable resources or optimize
network performance. In this work, we introduce a general methodology for
estimating lower and upper bounds for the policy-compliant path diversity and
bisection bandwidth between two nodes of a network, effectively quantifying the
effect of policies on these metrics. Exact values can be obtained if certain
conditions hold. The approach is based on regular languages and can be applied
in a variety of use cases.
