Is Selection Optimal for Scale-Free Small Worlds? Zs. Palotai a Cs. Farkas b A. Lőrincz a a Department of Information Systems, Eötvös Loránd University, Budapest, Hungary; b Department of Computer Science and Engineering, University of South Carolina, Columbia, S.C., USA A. Lőrincz Department of Information Systems, Eötvös Loránd University Pázmány Péter sétány 1/c, HU–1117 Budapest (Hungary) Tel. +36 1 209 0555/8473, Fax +36 1 381 2140, E-Mail andras.lorincz@elte.hu © 2006 S. Karger AG, Basel 1424–8492/06/0033–0158 $23.50/0 Complexus 2006;3:158–168 NETWORK MODELLING Key Words Scale-free small world  No free lunch theorem  Internet Abstract The ‘no free lunch theorem’ claims that for the set of all problems no algorithm performs better than random search and, thus, selection can be advantageous only on a limited set of problems. In this paper we investigate how the topo- logical structure of the environment influences algorithmic efficiency. We study the performance of algorithms, using selective learning, reinforcement learning, and their combinations, in random, scale-free, and scale-free small world (SFSW) environments. The learning problem is to search for novel, not-yet-found infor- mation. We ran our experiments on a large news site and on its downloaded portion. Controlled experiments were performed on this downloaded portion: we modified the topology, but preserved the publication time of the news. Our empirical results show that the selective learning is the most efficient in SFSW topology. In non-small world topologies, however, the combination of the se- lective and reinforcement learning algorithms performs the best. Copyright © 2006 S. Karger AG, Basel Published online: August 25, 2006 DOI: 10.1159/000094197 Fax +41 61 306 12 34 E-Mail karger@karger.ch www.karger.com Accessible online at: www.karger.com/cpu Simplexus A free lunch after all? Developers of web search engines and data mining tools expend vast sums at- tempting to find the most efficient ways for users to search. Mighty algorithms travail indexes with great speed and seemingly great efficacy, narrowing a key word search to a ‘short’ list of results within seconds. However, the ‘no free lunch theorem’ holds that there simply is no algorithm that can perform better than a random selection on the set of all problems. In other words, no matter how hard those developers try they will simply never beat a randomly selected set of ‘results’. In the present paper, Palotai, Farkas, and Lőrincz seek to understand how the topological structure of the environment influences algorithmic efficiency and whether or not there might be a ‘free’ lunch, after all. They compare the performance of algorithms in unearthing news from a large news website, using basic learning techniques – selective learning, reinforce- ment learning (RL), and their combina- tions, in random, scale-free, and scale-free small world (SFSW) environments. Their empirical results suggest that selective learning is the most efficient in SFSW to- pology, but in non-small world topologies, combining selective and RL algorithms gave the best results. Evolving systems, both natural and ar- tificial (like the Web), exhibit scale-free or SFSW properties. Previous researchers have shown that there is no performance difference between optimization or search algorithms if the algorithms are tested on every possible problem. This implies that differences in the performance of specific algorithms are simply a result of specific properties of the problem being looked at. By uncovering these properties, it should then be possible to develop optimized search approaches, despite the no free lunch theorem. The structure of a database or index is an important property and oth- ers have already demonstrated that an evo- Downloaded by: 54.237.89.119 - 5/7/2017 7:59:00 PM