CS267
Chris Pollett
Feb 17, 2021
u := -infty while u < infty do [u, v] := nextPhrase(t[1],t[2], .., t[n], u) if( u != infty) then report the interval [u, v]
function next(t, current) { // P[][] = array of posting list arrays // l[] = array of lengths of these posting lists static c = []; //last index positions for terms if(l[t] == 0 || P[t][l[t]] <= current) then return infty; if( P[t][1] > current) then c[t] := 1; return P[t][c[t]]; if( c[t] > 1 && P[t][c[t] - 1] <= current ) do low := c[t] -1; else low := 1; jump := 1; high := low + jump; while (high < l[t] && P[t][high] <= current) do low := high; jump := 2*jump; high := low + jump; if(high > l[t]) then high := l[t]; c[t] = binarySearch(t, low, high, current) return P[t][c[t]]; }
The book gives a nice analysis of the runtime returning all exact phrase matches when using this algorithm and shows it to be: `O(n cdot l cdot (log (L/l) + 1))`