Some Implementation Results on Random Polling Dynamic Load Balancing 2 Sequential Algorithms

Using two sample applications, we demonstrate the eeectiveness of our portable and reusable library for parallel tree search. On 1024 Transputers we achieve near optimal speedup even for quite small instances of the Golomb ruler problem. The 0/1 knapsack problem is more challenging but it is possible to achieve superlinear speedup compared to the standard sequential depth rst algorithm the implementation is based on. 1 The Problem Many algorithms in operations research and artiicial intelligence are based on depth rst search in implicitly deened trees. Since these problems are often very time consuming , parallelization is an attractive approach to extend the applicability of these algorithms. Unfortunately, the current status of parallel programming tools and the background of application programmers make an eeective parallelization diicult. This problem can be (partially) solved by encapsulating the parallelization into an application independent library. We outline the design and implementation of such a library and demonstrate its eeectiveness using the following two examples: A Golomb ruler 1] of length m with n marks at the integer positions 0 = m 1 , m 2 ,. .. , m n = m has the property jfm j ? m i : 1 i < j ngj = n(n ? 1)=2, i.e., the ruler can be used to measure a maximum number of distances. For a given n we want to nd a Golomb ruler with minimal m. These rulers have applications in interferometry and telematics. An instance of the 0-1 knapsack problem is deened by n items with weight w i and proot p i and a knapsack of capacity M. We are looking for x i 2 f0; 1g such that P p i x i is maximized subject to the constraint P w i x i M. Next to the traveling salesman problem, the knapsack problem might be one of the most extensively studied discrete optimization problems 5]. The Golomb ruler problem is solved using backtracking. On level i of the search tree mark i is placed. Starting from a trivial approach, we introduced a number of heuristics 1