# An analysis of budgeted parallel search on conditional Galton-Watson trees

## TL;DR

This paper investigates how limiting work per processor affects parallel tree search efficiency on conditional Galton-Watson trees, providing theoretical bounds and empirical validation for the budgeting technique.

## Contribution

It offers asymptotically tight bounds on the overhead caused by budgeting in parallel tree search on conditional Galton-Watson trees, supported by empirical results.

## Key findings

- Theoretical bounds on budgeting overhead are asymptotically tight.
- Empirical results confirm the accuracy of the theoretical bounds.
- Budgeting technique effectively balances workload and overhead in parallel tree search.

## Abstract

Recently Avis and Jordan have demonstrated the efficiency of a simple technique called budgeting for the parallelization of a number of tree search algorithms. The idea is to limit the amount of work that a processor performs before it terminates its search and returns any unexplored nodes to a master process. This limit is set by a critical budget parameter which determines the overhead of the process. In this paper we study the behaviour of the budget parameter on conditional Galton-Watson trees obtaining asymptotically tight bounds on this overhead. We present empirical results to show that this bound is surprisingly accurate in practice.