Efficient shifting on trees helps you partition a tree quickly and predictably.
This book explores the shifting algorithm for minimizing a partition on rooted and undirected trees. It introduces cuts, down-shifts, and side-shifts, and shows how a specialized data structure called a junction tree keeps track of changes. The work presents time bounds and practical ideas for updating structures as the algorithm runs, with a focus on performance.
- How the shifting algorithm assigns and moves cuts within a tree.
- How the junction-tree structure reflects changes and guides efficient updates.
- Time bounds that explain why certain steps run in constant or logarithmic time.
- The overall approach to achieving a min-max partition through iterative shifts.
Ideal for readers of advanced data structures and graph algorithms who want a concrete example of designing and analyzing a dynamic tree process.