Parallel Algorithms. Single Agent Search COMP 3705/4705. Parallel Search - Simple approaches. Dovetailing

Transcription

1 Parallel Algorithms Single Agent Search COMP 3705/4705 Prof. Nathan Sturtevant Lecture 15 For many years it looked like our problems would be solved by increases in processor speed Moore s law predicts the # of transistors, not the speed of the chip The number of transistors continues to grow Processor speed hasn t Parallel Search - Simple approaches Dovetailing IDA* One processor for each iteration Total speed up? (linear - at most 2x) DFBnB Bounds shared between processors Can be much faster, especially if better bounds are found Factor of Reduction in Nodes Expanded Best of Dovetailing Worst of Dovetailing Average of Dovetailing Candidate Set Size

2 Parallel Search: Abstraction Ratio of Nodes Expanded by Weight 7 To the Minimum Nodes Expanded Problem Number in the Order of Difficulty for Weight 7 Refine each portion separately Must go to common center point Parallel Search: Frontier Search Parallel Search - Simple approaches Most of the work on the first iteration Brute-force tree search Fixed branching factor, b Reduce from NlogN to N n processors Search to depth logbn Start one job for every processor

3 More Complicated Approaches Consider doing a breadth-first search of a large space Frontier search Space may be large enough to fit on disk, but not in memory Delayed Duplicate Detection Structured Duplicate Detection Example 1: 4-peg Tower of Hanoi No proven optimal recursive algorithm for generating solutions Want to verify optimal solution length Use frontier search to search solution space Frontier is up to 400GB (2TB) Example 2: 15 puzzle Perform breadth-first search of 15-puzzle DDD/SDD Iteratively generate frontiers Keep two levels at each point in time Task: Generate next search frontier, removing duplicates

4 DDD/SDD Frontier is stored on disk -- multiple files Broken into files based on state properties Hand-crafted or automatic hash function Location of the largest tiles Only have to look in the same file for duplicates Delayed Duplicate Detection Algorithm: Generate next frontier Put results in new files When finished, sort files & remove duplicates Delayed duplicated detection Remove old frontier and continue Structured Duplicate Detection Algorithm: For each file in frontier Load file & possible successor file Generate partial frontier Immediately remove duplicates May only load subset of successor files and do multiple passes generating successors Repeat for each file & through the frontier Parallelism Any of the frontier files can be worked on in any order One processor for each frontier file New positions are generated in all frontier files Writes are just appends to files, which are synchronized by file system Easy concurrency!

5 Abstraction Work is divided according to the abstraction TOH: Position of the largest disks Could be state in pattern database First case is easier because: Opened/closed nodes remain distinct Not looking for a solution, only the solution length Structured Duplicate Detection Use single abstraction of problem space Abstraction is a graph Every state maps into graph Need to write/read open/closed lists Managing read-writes Use abstract graph to limit where successors fall Lock states & neighbors when expanding Lock only needed on abstract graph In A* all the nodes with the same f-value will be expanded in parallel Algorithm For each processor: Get lock on abstract graph to: Find a node with count of 0 Mark neighbors as locked Expand all nodes in abstract node s bucket Get lock & release counts Repeat

6 Large BFS - Other enhancements Don t store nodes will all operators are forbidden 12-16% storage reduction 5% IO reduction Interleaving expansion & merging Perform duplicate detection once all states for a file are generated Large BFS - Fault Tolerance Easy: Keep all of previous iteration until next iteration finished (2x memory) Harder: Don t delete files until finished with them If a merge (duplicate detection) is in process, it will be restarted If generating children is in process, children will be regenerated UPS to make sure buffers can be flushed Disk Errors Errors for every bits written Some can be recovered by checksums 8x10 14 bits written by complete search of 15-puzzle Expect frequent errors Use RAID to reduce errors 28 days 8 hours total, 1.4 TB of disk required Applications to A* Can use the same ideas for A* search May not expand nodes in a best-first order Work may be too focused to gain good parallelization