Linear ordering of objects is important in many applications.
For example, destined to live with the RAM model of computing for a foreseeable future, optimal linear ordering of elements to improve cache coherency and performance of out of core algorithms becomes crucial. While ordering the elements, the access pattern has to be taken into
account, which in turn is application dependent. Assuming, between
pairs of elements, we have the probability estimates of the second
element being accessed after the first, we propose a solution to the
problem of linear ordering of elements using 1-factor graph
partitioning algorithm.

Primarily, we will motivate the need for linear ordering using its
application to various problems in computer graphics including cache-coherent triangle ordering (also called stripification), simplification,
compression, efficient back-face culling, quadrilateral mesh
stripification, and tetrahedral mesh stripification. In simplicial
complex realization of manifold spaces, the algorithm can be extended
to generate space-filling curves. The graph abstraction of the
problem makes the solution seamlessly extendable to elements in
higher dimensions including higher dimensional databases and nodes of
the hierarchical partitioning of the objects like quadtrees and
octrees in computer graphics.