Conjunctive Queries

Evaluating CSP’s having bounded
(gen.) hypertree width
k fixed
Given:
a database db of relations
a CSP Q over db such that hw(Q) k or ghw k
a width k hypertree decomposition of Q
• Deciding whether (Q,db) solvable is in
O(n k+1 log n) and complete for LOGCFL
• Computing Q(db) is feasible in
output-polynomial time
Observation: If H has n vertices, then
HW(H)n/2+1
Does not hold for TW: TW(K n )=n-1
Often HW < TW. H-Decomps are interesting
In case of bounded arity, too.
ComparingDecompositionMethods
We compare these methods according to
their ability in indentifying tractable classes of
CSP instances:
Comparison results
Hypertree Decomposition
• D1 D2 (D2generalizes D1):
0suchthat, k>0,C(D1,k) C(D2,k+)
everyclassofCSPstractableaccordingtoD1istractableaccordingtoD2,
according to is according to D2
with(almost)thesamecost.
• D2
D1 (D2beats D1):thereexistsanintegerksuchthat
exists integer such that
m,C(D2,k) C(D1,m)
thereareclassesofCSPstractableaccordingtoD2butnottractable
accordingtoD1.
• D1