JOURNAL OF INFORMATION SCIENCE AND ENGINEERING 26, 1231-1242 (2010) 1231 Oriented Networks Design Problem JEROME GALTIER 1 , IGOR PESEK 2 , KATJA PRNAVER 3 AND JANEZ ŽEROVNIK 3,4 1 Orange Labs 905 rue Albert Einstein 06921 Sophia Antipolis Cedex, France 2 Faculty of Natural Sciences and Mathematics University of Maribor Koroška 160,2000 Maribor, Slovenia 3 Institute of Mathematics, Physics and Mechanics Jadranska 19, 1000 Ljubljana, Slovenia 4 Faculty of Mechanical Engineering University of Ljubljana Aškerčeva 6, 1000 Ljubljana, Slovenia The design of interconnection networks is very popular in computer science. In this paper we introduce a novel problem, the design of oriented networks. The underlying structure of such networks is a directed graph with weights on the arcs, which are the number of paths of the routing that traverse the arc. The cost of a network with a routing is defined as a sum of arc costs that are computed with concave increasing cost function depending on weights over directed arcs. The objective is to find the routing that is op- timal in terms of costs. The corresponding minimization problem is approached with a local search type heuristics. New local search neighborhood is defined and analyzed. Keywords: oriented networks problem, heuristics, local search, hill climbing, SDH net- works 1. INTRODUCTION One of the most popular applications of graph theory in computer science is the de- sign of interconnection networks. A desirable network is usually optimal with respect to the value of one (or more) graph invariants, for example it has small diameter, small av- erage distance and small routing costs or allows uniform distribution of traffic. In this paper we look closely at the oriented network design problem [1] that arises in the design of SDH loop networks [4, 5]. Synchronous Digital Hierarchy (SDH) is a multiplexing protocol for transferring multiple digital bit streams using lasers or light-emitting diodes (LEDs) over the same optical fiber. SDH standard was developed by the International Telecommunication Union (ITU), and is documented in standard G.707 and its extension G.708. In such networks, the traffic requests are routed along a set of containers of fixed capacity, where each container connects two nodes of the network. The cost of the network is defined as the sum of arc contributions, where the arc contribution is a certain power (w(e) α , 0 ≤ α ≤ 1) of the number of paths (of the routing) traversing the arc. Practitioners discovered that using a concave increasing cost function of the form w(e) α accurately de- scribes the problem. Consequently, the cost depends only on the capacity and no cost of Received July 11, 2008; revised October 20, 2008 & January 5 & May 7 & June 19, 2009; accepted July 10, 2009. Communicated by Nancy M. Amato.