Sound Complete LinearSpace BestFirst Diagnosis Search DX 20
Sound, Complete, Linear-Space, Best-First Diagnosis Search DX’ 20 Patrick Rodler
Diagnosis Computation desired # of leading diagnoses to be computed e. g. : most-prob or min-card diagnoses opt criterion (max prob or min card), component probs, etc. This is the problem we solve in this work! DPI = diagnosis problem instance <SD, COMPS, OBS> DPI diagnosis computation algorithm meta info only min diagoses all min diagnoses (given sufficient time + space) existing methods: desired properties: (i. a. ) + [Abreu, van Gemund, 2009] e. g. , HS-Tree completeness [Reiter, 1987] + ++ best-first property + • soundness • e. g. , STACCATO diagnoses enumerated in order as per opt criterion • independence of used • SD language • theorem prover • generality / broad applicability • time efficiency • space efficiency DX‘ 20 no algorithms that feature all properties there are sound + complete + general + space-efficient algorithms there are sound + timeefficient + space-efficient algorithms (many other combinations) WHENEVER sound + complete + best-first + e. g. , Inv-HS-Tree [Schekotihin et al, 2014] general, THEN exponential space + + Sound, Complete, Linear-Space, Best-First Diagnosis Search 2
New Linear-Space Approach – RBF-HS space efficiency is important if, e. g. , – minimal diagnoses have high cardinality – little memory is available (large search space) (e. g. , on low-end microprocessors, cf. Io. T) as a remedy, we suggest RBF-HS (Recursive Best-First Hitting Set) search – based on well-known RBFS (Recursive Best-First Search) [Korf, 1992] – sound + complete + best-first + general + linear-space principle: recursive best-first downwards exploration + backtracking + node cost update – complete and best-first: always expand current globally-best node while remembering current globally-2 nd-best node – undo + forget to keep space linear: backtrack + explore 2 nd-best node if none of child nodes of best node is better than 2 nd-best – remember utility of forgotten subtrees to keep search progressing: before deleting a subtree when backtracking, store cost of subtree’s best node – restore utility at node regeneration to avoid redundancy: whenever a subtree is re-explored, use stored cost value to update node costs in subtree DX‘ 20 Sound, Complete, Linear-Space, Best-First Diagnosis Search 3
RBF-HS – Principle best…highest prob among all open nodes root node = min conflict locally best…highest prob among all child nodes successor generation like in Reiter‘s HS-Tree: one successor for each element of min conflict better…higher prob best locally 2 nd best locally best globally 2 nd best locally 2 nd best which is better? propagate downwards globally 2 nd best locally best ✔ node‘s prob first hitting set found! necessarily min diag necessarily most prob DX‘ 20 propagate downwards update prob backtrack, but remember prob of best child linear space: no more than one expanded node at each tree level! condition: “cost-adjustment“ = each component must have prob < 0. 5 Sound, Complete, Linear-Space, Best-First Diagnosis Search 4
Example (RBF-HS in Action) node generation numbers DX‘ 20 node probability computed min diagnoses probability of globally 2 nd-best node “bound” Sound, Complete, Linear-Space, Best-First Diagnosis Search 5
Example (RBF-HS in Action) DX‘ 20 Sound, Complete, Linear-Space, Best-First Diagnosis Search 6
Example (RBF-HS in Action) DX‘ 20 Sound, Complete, Linear-Space, Best-First Diagnosis Search 7
Example (RBF-HS in Action) DX‘ 20 Sound, Complete, Linear-Space, Best-First Diagnosis Search 8
Example (RBF-HS in Action) DX‘ 20 Sound, Complete, Linear-Space, Best-First Diagnosis Search 9
Example (RBF-HS in Action) DX‘ 20 Sound, Complete, Linear-Space, Best-First Diagnosis Search 10
Example (RBF-HS in Action) DX‘ 20 Sound, Complete, Linear-Space, Best-First Diagnosis Search 11
Example (RBF-HS in Action) DX‘ 20 Sound, Complete, Linear-Space, Best-First Diagnosis Search 12
Evaluation to access the implementation of the algorithm, please visit: https: //bit. ly/2 Gp 3 Xw. X test RBF-HS on 11 different logics Reiter’s HS-Tree all beyond NP-complete, up to 2 -NEXPTIME-complete # components |COMPS| DX‘ 20 complexity of consistency check (roughly: more letters, higher complexity) Sound, Complete, Linear-Space, Best-First Diagnosis Search # min diags --------- size mincard diag --------- size maxcard min diag 13
Results • e. g. : 88% runtime savings, 97% memory savings diagnosis problems well-understood phenomenon: [Zhang, Korf, 1995] when priority queue management (linear in tree depth) in HS-Tree is more expensive than node regenerations in RBF-HS DX‘ 20 Sound, Complete, Linear-Space, Best-First Diagnosis Search 14
Conclusions problem: whenever diagnosis search is then it requires sound + complete + best-first + generally applicable exponential space solution: RBF-HS = sound + complete + best-first + generally applicable + linear-space results: for min-card diagnosis computation • substantial space savings • often both time + space savings compared to HS-Tree (sound + complete + best-first + generally applicable) DX‘ 20 Sound, Complete, Linear-Space, Best-First Diagnosis Search 15
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