CS267
Chris Pollett
Sep 12, 2018
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))`
function binarySearch($t, $P, $low, $high, $current)and implements the binary search which could be used as part of a PHP implementation of the next(t, current) function of the previous slide.
$t = "dog"; $P = [ "cat" => [1, 6, 7], "dog" => [1 ,2, 23, 25, 27, 50] ]; echo binarySearch($t, $P, 1, 4, 15);
When working with documents there are several common statistics which people typically keep track of:
Also, when working with document-oriented indexes it is common to support coarser grained methods in our ADT, such as firstDoc(`t`), lastDoc(`t`), nextDoc(`t`, `mbox(current)`), and prevDoc(`t`, `mbox(current)`). The idea of a method like nextDoc, is that it returns the first document with the term `t` after `current` in the corpus. i.e., we don't care about position in the document with this method.