Ten Conferences WORDS: Open Problems and Conjectures

In connection to the development of the field of Combinatorics on Words, we present a list of open problems and conjectures that were stated during the ten last meetings WORDS. We wish to continually update the present document by adding informations concerning advances in problems solving

The Collatz conjecture and De Bruijn graphs

We study variants of the well-known Collatz graph, by considering the action of the 3n+1 function on congruence classes. For moduli equal to powers of 2, these graphs are shown to be isomorphic to binary De Bruijn graphs. Unlike the Collatz graph, these graphs are very structured, and have several interesting properties. We then look at a natural generalization of these finite graphs to the 2-adic integers, and show that the isomorphism between these infinite graphs is exactly the conjugacy map previously studied by Bernstein and Lagarias. Finally, we show that for generalizations of the 3n+1 function, we get similar relations with 2-adic and p-adic De Bruijn graphs.Comment: 9 pages, 8 figure

Overview of the 2005 cross-language image retrieval track (ImageCLEF)

The purpose of this paper is to outline efforts from the 2005 CLEF crosslanguage image retrieval campaign (ImageCLEF). The aim of this CLEF track is to explore the use of both text and content-based retrieval methods for cross-language image retrieval. Four tasks were offered in the ImageCLEF track: a ad-hoc retrieval from an historic photographic collection, ad-hoc retrieval from a medical collection, an automatic image annotation task, and a user-centered (interactive) evaluation task that is explained in the iCLEF summary. 24 research groups from a variety of backgrounds and nationalities (14 countries) participated in ImageCLEF. In this paper we describe the ImageCLEF tasks, submissions from participating groups and summarise the main fndings

Parallel String Sample Sort

We discuss how string sorting algorithms can be parallelized on modern multi-core shared memory machines. As a synthesis of the best sequential string sorting algorithms and successful parallel sorting algorithms for atomic objects, we propose string sample sort. The algorithm makes effective use of the memory hierarchy, uses additional word level parallelism, and largely avoids branch mispredictions. Additionally, we parallelize variants of multikey quicksort and radix sort that are also useful in certain situations.Comment: 34 pages, 7 figures and 12 table