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## Appendix: Hierarchical Partitioning (HIER)

### Outline of Algorithm

Zoltan's hierarchical balancing automates the creation of hierarchical partitions. The implementation of Hierarchical Partitioning (HIER) in Zoltan is due to Jim Teresco (Williams College), with many suggestions and ideas from the entire Zoltan team.

The hierarchical balancing implementation utilizes a lightweight intermediate structure and a set of callback functions that permit an automated and efficient hierarchical balancing which can use any of the procedures available within Zoltan without modification and in any combination. Hierachical balancing is invoked by an application the same way as other Zoltan procedures. Since Zoltan is data-structure neutral, it operates on generic "objects" and interfaces with applications through callback functions.

A hierarchical balancing step begins by building an intermediate structure using the application-supplied callbacks. The initial structure is computed using Zoltan_Build_Graph to build the same structure that is used to support partitioning using the Parmetis and Jostle libraries. The hierarchical balancing procedure then provides its own callback functions to allow existing Zoltan procedures to be used to query and update the intermediate structure at each level of a hierarchical balancing. The structure is augmented to keep track of objects and their needed information during the procedure. After all levels of the hierarchical balancing have been completed, Zoltan's usual migration arrays are constructed and returned to the application. Thus, only lightweight objects are migrated internally between levels, not the (larger and more costly) application data. More details about the fields of the intermediate structure and how the are used can be found in the Zoltan distribution in hier/README.

### Data Structure Definitions

There is one major data structure in HIER, defined in hier/hier.h. The struct HierPartParamsStruct includes all information needed by the hierarchical balancing procedures. The fields are documented in comments in the structure definition.

### Parameters

The parameters used by HIER and their default values are described in the HIER section of the Zoltan User's Guide. These can be set by use of the Zoltan_Hier_Set_Param subroutine in the file hier/hier.c.

### Main Routine

The main routine for HIER is Zoltan_Hier in the file hier/hier.c.

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