In this paper we review the traversal algorithms for kd-trees for ray tracing. Ordinary traversal algorithms such as sequential, recursive, and those with neighbor-links have different limitations, which led to several new developments within the last decade. We describe algorithms exploiting ray coherence and algorithms designed with specific hardware architecture limitations such as memory la...

Recently, the classical backtracking-search satis ability algorithm of Davis, Putnam, Loveland and Logemann (DPLL) has been enhanced in two distinct directions: with more advanced reasoning methods, or with con ict-directed back-jumping (CBJ). Previous methods used one idea or the other, but not both (except that CBJ has been combined with the unit-clause rule). The diÆculty is that more advanc...

We present an orthogonal topological framework which is able to provide incidence traversal operations for all topological elements. The run-time performance of this topological traversal operations can be optimized at a highly expressive level, where the abstraction penalty imposed by this approach is negligible. For the topological storage we use vertex-cell as well as cell-vertex incidence i...

This thesis will present a number of results related to path traversal in trees and graphs. In particular, we focus on data structures which allow such traversals to be performed efficiently in the external memory setting. In addition, for trees and planar graphs the data structures we present are succinct. Our tree structures permit efficient bottom-up path traversal in rooted trees of arbitra...