Parallel backtracking with answer memoing for independent and-parallelism

Abstract

Goal-level Independent and-parallelism (IAP) is exploited by scheduling for simultaneous execution two or more goals which will not interfere with each other at run time. This can be done safely even if such goals can produce multiple answers. The most successful IAP implementations to date have used recomputation of answers and sequentially ordered backtracking. While in principle simplifying the implementation, recomputation can be very inefficient if the granularity of the parallel goals is large enough and they produce several answers, while sequentially ordered backtracking limits parallelism. And, despite the expected simplification, the implementation of the classic schemes has proved to involve complex engineering, with the consequent difficulty for system maintenance and extension, while still frequently running into the well-known trapped goal and garbage slot problems. This work presents an alternative parallel backtracking model for IAP and its implementation. The model features parallel out-of-order (i.e., non-chronological) backtracking and relies on answer memoization to reuse and combine answers. We show that this approach can bring significant performance advantages. Also, it can bring some simplification to the important engineering task involved in implementing the backtracking mechanism of previous approaches.

A Segment-Swapping Approach for Executing Trapped Computations

“…Note that, while we have discussed so far approaches which keep the sequential solution order, trapped computations also appear in approaches to and-parallelism which give up on maintaining sequential execution solution order [20]. Therefore this paper is not as much a quest for efficiency as an attempt to find a simple solution (which minimizes changes to the scheduler while keeping the performance of the sequential execution) to a problem which seems unavoidable in and-parallel execution.…”

“…We have used some deterministic and non-deterministic benchmarks selected from [28,20], listed in Table 1. All these benchmarks can produce trapped goals (i.e., goals stacked out of order w.r.t.…”

“…Instead, the proposed solution seems more practical since it greatly simplifies the parallel scheduler (with the added advantage, discussed later, that it can be reused for other purposes). This is even more so if we take into account that the frequency of trapped goals can be largely reduced by out-of-order backtracking with answer memoization [20], in which the traditional rightto-left order in backtracking is not maintained on parallel goal conjunctions. In this case the stack reorganization operation, although still necessary, is used even less frequently.…”

“…In addition, the execution based on goal precedence of our prototype has been shown to be quite sensitive to the order in which the parallel goals are taken by remote agents, which makes the overall speed of the parallel execution less predictable. Finally, this solution is intended to match the behavior of standard sequential execution and is of no use in the case of strategies which use less strict execution strategies to increase the amount of search performed in parallel [20]. Therefore, we believe that avoiding trapped goals based on goal precedence has drawbacks which makes it not advantageous in practice.…”