From mboxrd@z Thu Jan 1 00:00:00 1970 Return-Path: X-Original-To: caml-list@yquem.inria.fr Delivered-To: caml-list@yquem.inria.fr Received: from nez-perce.inria.fr (nez-perce.inria.fr [192.93.2.78]) by yquem.inria.fr (Postfix) with ESMTP id 34CD2BBBB for ; Fri, 31 Mar 2006 15:42:43 +0200 (CEST) Received: from pauillac.inria.fr (pauillac.inria.fr [128.93.11.35]) by nez-perce.inria.fr (8.13.0/8.13.0) with ESMTP id k2VDggJ0030765 for ; Fri, 31 Mar 2006 15:42:42 +0200 Received: from nez-perce.inria.fr (nez-perce.inria.fr [192.93.2.78]) by pauillac.inria.fr (8.7.6/8.7.3) with ESMTP id PAA24291 for ; Fri, 31 Mar 2006 15:42:41 +0200 (MET DST) Received: from justus.rz.uni-saarland.de (justus.rz.uni-saarland.de [134.96.7.31]) by nez-perce.inria.fr (8.13.0/8.13.0) with ESMTP id k2VDgfC0030762 for ; Fri, 31 Mar 2006 15:42:41 +0200 Received: from uni-sb.de (uni-sb.de [134.96.7.230]) by justus.rz.uni-saarland.de (8.12.11.20060308/8.12.10) with ESMTP id k2VDgejY20458167; Fri, 31 Mar 2006 15:42:40 +0200 (CEST) Received: from mail.cs.uni-sb.de (mail.cs.uni-sb.de [134.96.254.200]) by uni-sb.de (8.13.6/2006032300) with ESMTP id k2VDgdJx020708; Fri, 31 Mar 2006 15:42:39 +0200 (CEST) Received: from mail.st.cs.uni-sb.de (goscinny.cs.uni-sb.de [134.96.235.32]) by mail.cs.uni-sb.de (8.13.6/2006032300) with ESMTP id k2VDgdRA027370; Fri, 31 Mar 2006 15:42:39 +0200 (CEST) Received: from [134.96.235.101] (jonagold.cs.uni-sb.de [134.96.235.101]) by mail.st.cs.uni-sb.de (Postfix) with ESMTP id 5F30B1BD87; Fri, 31 Mar 2006 15:42:39 +0200 (CEST) In-Reply-To: References: Mime-Version: 1.0 (Apple Message framework v623) Content-Type: text/plain; charset=US-ASCII; format=flowed Message-Id: Content-Transfer-Encoding: 7bit Cc: Caml List From: Christian Lindig Subject: Re: [Caml-list] efficient binary relations? Date: Fri, 31 Mar 2006 15:42:37 +0200 To: Sebastian Egner X-Mailer: Apple Mail (2.623) X-Greylist: Sender IP whitelisted, not delayed by milter-greylist-1.5.1 (justus.rz.uni-saarland.de [134.96.7.31]); Fri, 31 Mar 2006 15:42:40 +0200 (CEST) X-AntiVirus: checked by AntiVir Milter (version: 1.1.1-9; AVE: 6.34.0.14; VDF: 6.34.0.124; host: AntiVir2) X-Miltered: at nez-perce with ID 442D31D2.000 by Joe's j-chkmail (http://j-chkmail.ensmp.fr)! X-Miltered: at nez-perce with ID 442D31D1.001 by Joe's j-chkmail (http://j-chkmail.ensmp.fr)! X-Spam: no; 0.00; lindig:01 lindig:01 binary:01 computes:01 applicative:01 cubic:98 wrote:01 uni-sb:01 caml-list:01 structures:01 data:02 data:02 clarify:02 functional:02 suggestion:03 X-Spam-Checker-Version: SpamAssassin 3.0.3 (2005-04-27) on yquem.inria.fr X-Spam-Level: X-Spam-Status: No, score=0.0 required=5.0 tests=none autolearn=disabled version=3.0.3 On Mar 31, 2006, at 2:50 PM, Sebastian Egner wrote: > Please could you clarify the circumstances a little bit? > > 1. Are you looking for a data structure that you set > up for a fixed R once and then query many times for > different X? Or are you looking for a dynamic data > structure in which you keep changing R? Or are you > looking for a 'functional data structure' where the > older versions of R are preserved? Or for a functional > data structure where R is fixed, but the queries X > are constructed incrementally? > > 2. Is R sparse, i.e. is |R| << |\X|*|\Y|? First, thanks for a detailed suggestion! R is sparse, constructed once, and queried often. As I mentioned, this is in the context of concept analysis. The ' operation computes the maximal blocks (or concepts) in a cross table; typically their number grows cubic with the size |R| of the relation - hence the importance of the ' operation. (In the worst case, when the matrix is densely populated, there may be exponentially many blocks.) I generally prefer applicative data structures (without side effects) but understand that this is not always possible. -- Christian