On the Generation of Heronian Triangles

We describe several algorithms for the generation of integer Heronian triangles with diameter at most n. Two of them have running time O(n^(2+ε)). We enumerate all integer Heronian triangles for n ≤ 600000 and apply the complete list on some related problems.

Effectiveness of Title-Search vs. Full-Text Search in the Web

Search engines sometimes apply the search on the full text of documents or web-pages; but sometimes they can apply the search on selected parts of the documents only, e.g. their titles. Full-text search may consume a lot of computing resources and time. It may be possible to save resources by applying the search on the titles of documents only, assuming that a title of a document provides a concise representation of its content. We tested this assumption using Google search engine. We ran search queries that have been defined by users, distinguishing between two types of queries/users: queries of users who are familiar with the area of the search, and queries of users who are not familiar with the area of the search. We found that searches which use titles provide similar and sometimes even (slightly) better results compared to searches which use the full-text. These results hold for both types of queries/users. Moreover, we found an advantage in title-search when searching in unfamiliar areas because the general terms used in queries in unfamiliar areas match better with general terms which tend to be used in document titles.

Constructing 7-Clusters

ACM Computing Classification System (1998): G.2, G.4.

Approximating the MaxMin and MinMax Area Triangulations using Angular Constraints

* A preliminary version of this paper was presented at XI Encuentros de Geometr´ia Computacional, Santander, Spain, June 2005.