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SA RT AGNAN A PARALLEL PORTFOLIO SAT SOLVER WITH LOCKLESS PHYSICAL CLAUSE SHARING Stephan Kottler and Michael Kaufmann University of Tuebingen 1—KOTTLER,KAUFMANN (SARTAGNAN)
SARTAGNANA PARALLEL PORTFOLIO SAT SOLVER
WITH LOCKLESS PHYSICAL CLAUSE SHARING
Stephan Kottler and Michael Kaufmann
University of Tuebingen
1 — KOTTLER, KAUFMANN (SARTAGNAN)
OUTLINE
1 MOTIVATION
2 PARALLEL SOLVINGPhysical clause sharingCommunication of threads
3 PORTFOLIO SOLVING
4 SUMMARY
2 — KOTTLER, KAUFMANN (SARTAGNAN)
I MOTIVATION
STATE-OF-THE-ART SOLVINGCDCL
partial assignmentdecisions based on variable activityconflict analysisrestarts
DMRPcomplete assignment (ref. point)
decisions based on unsat clauses
slower than CDCL but less decisions
3 — KOTTLER, KAUFMANN (SARTAGNAN)
I MOTIVATION
STATE-OF-THE-ART SOLVINGCDCL
partial assignmentdecisions based on variable activityconflict analysisrestarts
DMRPcomplete assignment (ref. point)
decisions based on unsat clauses
slower than CDCL but less decisions
3 — KOTTLER, KAUFMANN (SARTAGNAN)
I MOTIVATION
KINDS OF PARALLELISATIONDivision of search space (guiding path)Portfolio solving
CLAUSE SHARINGMost solvers: copy learnt clauses of other threads
MAIN AIMReal / physical sharing of dataThreads work together⇒ Any thread may benefit from strengthened clauseNo use of OS locks
4 — KOTTLER, KAUFMANN (SARTAGNAN)
I MOTIVATION
KINDS OF PARALLELISATIONDivision of search space (guiding path)Portfolio solving
CLAUSE SHARINGMost solvers: copy learnt clauses of other threads
MAIN AIMReal / physical sharing of dataThreads work together⇒ Any thread may benefit from strengthened clauseNo use of OS locks
4 — KOTTLER, KAUFMANN (SARTAGNAN)
II PARALLEL SOLVING
BASIC CONCEPT TO SHARE DATA
Shared data / objects contain user-maskuser-mask initialised by creating threadAny thread can release object (clear bit)Last thread destructs object
Compare and Swap operation
void release(SharedObj obj, tId){do{
SharedObj{ old = obj.umask;umask; new = clear bit ’tId’ in old;... }while(!exchange(obj.umask,old,new));} if(new == 0) destruct(obj);
}
5 — KOTTLER, KAUFMANN (SARTAGNAN)
II PARALLEL SOLVING
BASIC CONCEPT TO SHARE DATA
Shared data / objects contain user-maskuser-mask initialised by creating threadAny thread can release object (clear bit)Last thread destructs object
Compare and Swap operationvoid release(SharedObj obj, tId){do{
SharedObj{ old = obj.umask;umask; new = clear bit ’tId’ in old;... }while(!exchange(obj.umask,old,new));} if(new == 0) destruct(obj);
}
5 — KOTTLER, KAUFMANN (SARTAGNAN)
II.A PHYSICAL CLAUSE SHARINGII PARALLEL SOLVING
PHYSICAL SHARING OF CLAUSESHave one instance of a clauseIndirection to access clause (thread private data)
6 — KOTTLER, KAUFMANN (SARTAGNAN)
II.A PHYSICAL CLAUSE SHARINGII PARALLEL SOLVING
SHARED CLAUSE’ ARCHITECTURE
7 — KOTTLER, KAUFMANN (SARTAGNAN)
II.A PHYSICAL CLAUSE SHARINGII PARALLEL SOLVING
REFERENCING CLAUSES IN CDCLUnit propagationConflict analysisGarbage collection
OBSERVATIONWhenever a clause is referenced at least onewatched literal is known
LEMMATwo watched literals li , lj can be stored by one value:Cw = li xor lj .(li xor Cw → lj )
8 — KOTTLER, KAUFMANN (SARTAGNAN)
II.A PHYSICAL CLAUSE SHARINGII PARALLEL SOLVING
REFERENCING CLAUSES IN CDCLUnit propagationConflict analysisGarbage collection
OBSERVATIONWhenever a clause is referenced at least onewatched literal is known
LEMMATwo watched literals li , lj can be stored by one value:Cw = li xor lj .(li xor Cw → lj )
8 — KOTTLER, KAUFMANN (SARTAGNAN)
II.A PHYSICAL CLAUSE SHARINGII PARALLEL SOLVING
REFERENCING CLAUSES IN CDCLUnit propagationConflict analysisGarbage collection
OBSERVATIONWhenever a clause is referenced at least onewatched literal is known
LEMMATwo watched literals li , lj can be stored by one value:Cw = li xor lj .(li xor Cw → lj )
8 — KOTTLER, KAUFMANN (SARTAGNAN)
II.A PHYSICAL CLAUSE SHARINGII PARALLEL SOLVING
SHARED CLAUSE’ ARCHITECTURE II
9 — KOTTLER, KAUFMANN (SARTAGNAN)
II.A PHYSICAL CLAUSE SHARINGII PARALLEL SOLVING
DIGRESS TO SEQUENTIAL SOLVERSOrder of literals may be modifiedStore clause C with |C|−1 integers
10 — KOTTLER, KAUFMANN (SARTAGNAN)
II.A PHYSICAL CLAUSE SHARINGII PARALLEL SOLVING
OVERHEAD OF CLAUSE ORGANISATIONComparison of different implementations with single thread
11 — KOTTLER, KAUFMANN (SARTAGNAN)
II.B COMMUNICATION OF THREADSII PARALLEL SOLVING
COMMUNICATION OF THREADS
Message queues used to send . . .a new clause (may be new version)notification on variable eliminationvariable replacementheuristic information
! Messages not only for heuristics! Keep order of messages! No OS locks
12 — KOTTLER, KAUFMANN (SARTAGNAN)
II.B COMMUNICATION OF THREADSII PARALLEL SOLVING
COMMUNICATION OF THREADS
Message queues used to send . . .a new clause (may be new version)notification on variable eliminationvariable replacementheuristic information
! Messages not only for heuristics! Keep order of messages! No OS locks
12 — KOTTLER, KAUFMANN (SARTAGNAN)
II.B COMMUNICATION OF THREADSII PARALLEL SOLVING
LOCKLESS QUEUESone reading / one writing threadwriteHead points to next write positionreadHead points to next read positionqueue empty if writeHead = readHead
13 — KOTTLER, KAUFMANN (SARTAGNAN)
II.B COMMUNICATION OF THREADSII PARALLEL SOLVING
LOCKLESS QUEUESone reading / one writing threadwriteHead points to next write positionreadHead points to next read positionqueue empty if writeHead = readHead
13 — KOTTLER, KAUFMANN (SARTAGNAN)
II.B COMMUNICATION OF THREADSII PARALLEL SOLVING
LOCKLESS QUEUESone reading / one writing threadwriteHead points to next write positionreadHead points to next read positionqueue empty if writeHead = readHead
13 — KOTTLER, KAUFMANN (SARTAGNAN)
II.B COMMUNICATION OF THREADSII PARALLEL SOLVING
LOCKLESS QUEUESone reading / one writing threadwriteHead points to next write positionreadHead points to next read positionqueue empty if writeHead = readHead
13 — KOTTLER, KAUFMANN (SARTAGNAN)
II.B COMMUNICATION OF THREADSII PARALLEL SOLVING
LOCKLESS QUEUESone reading / one writing threadwriteHead points to next write positionreadHead points to next read positionqueue empty if writeHead = readHead
13 — KOTTLER, KAUFMANN (SARTAGNAN)
II.B COMMUNICATION OF THREADSII PARALLEL SOLVING
DYNAMIC SIZEWrite operation may failWrite operation may overwrite unseen data
IDEAQueue links to available update
Queue hasseveral readingthreads!
14 — KOTTLER, KAUFMANN (SARTAGNAN)
II.B COMMUNICATION OF THREADSII PARALLEL SOLVING
DYNAMIC SIZEWrite operation may failWrite operation may overwrite unseen data
IDEAQueue links to available update
Queue hasseveral readingthreads!
14 — KOTTLER, KAUFMANN (SARTAGNAN)
II.B COMMUNICATION OF THREADSII PARALLEL SOLVING
DYNAMIC SIZEWrite operation may failWrite operation may overwrite unseen data
IDEAQueue links to available update
Queue hasseveral readingthreads!
14 — KOTTLER, KAUFMANN (SARTAGNAN)
II.B COMMUNICATION OF THREADSII PARALLEL SOLVING
DYNAMIC SIZEWrite operation may failWrite operation may overwrite unseen data
IDEAQueue links to available update
Queue hasseveral readingthreads!
14 — KOTTLER, KAUFMANN (SARTAGNAN)
III PORTFOLIO SOLVING
DIFFERENT STRATEGIES
6 of 8 threads apply CDCL (different settings)Activity of Variables / LiteralsGlucose / Static / Geometric / Luby restart schemes
Dedicated simplification threadsatElite like simplificationAsymmetric branching / vivificationSCC computation and removal of redundant binaries
Connect work - DMRPAt each restart: init reference point to set eachvariable to predominant value among all threadsLearn ’interesting’ clauses
15 — KOTTLER, KAUFMANN (SARTAGNAN)
III PORTFOLIO SOLVING
TAKE ADVANTAGE OF SHARING
Simplification of clause DB is sharedimmediatelyOn-the-fly clause subsumption done by anythread⇒ Any thread may benefitLazy hyper binary resolution
16 — KOTTLER, KAUFMANN (SARTAGNAN)
III PORTFOLIO SOLVING
DMRP & LITERALS ACTIVITY
17 — KOTTLER, KAUFMANN (SARTAGNAN)
IV SUMMARY
SUMMARY
Physical clause sharingXOR idea to store watched literalsparallel and sequential solvers
Communication without OS locks
CHALLENGES! Has to run in parallel
Difficult to measure speedupComputation time
? Logging without influencing course of events
18 — KOTTLER, KAUFMANN (SARTAGNAN)
IV SUMMARY
CLAUSE COPYING STILL FASTER
Thank you for your attention!
19 — KOTTLER, KAUFMANN (SARTAGNAN)
MotivationParallel SolvingPhysical clause sharingCommunication of threads
Portfolio SolvingSummary
