Abstract-The Traveling Salesman Problem (TSP) is the problem of finding the shortest path passing through all given cities while only passing by each city once and finishing at the same starting city. This problem has NP-hard complexity making it extremely impractical to get the most optimal path even for problems as small as 20 cities since the number of permutations becomes too high. Many heuristic methods have been devised to reach "good" solutions in reasonable time. In this paper, we present the idea of utilizing a spatial "geographical" Divide and Conquer technique in conjunction with heuristic TSP algorithms specifically the Nearest Neighbor 2-opt algorithm. We have found that the proposed algorithm has lower complexity than algorithms published in the literature. This comes at a lower accuracy expense of around 9%. It is our belief that the presented approach will be welcomed to the community especially for large problems where a reasonable solution could be reached in a fraction of the time.
The informal economy occupies a major position in the structure of urban communities, its presence and intensity poses many problems and challenges for the development of urban communities. For the importance of the spatial dimension of informal economy activities and the overlapping issues of informal housing, unemployment, poverty and social marginalization… etc., we must study the dynamic relationship between informal sector activities and housing system. The first part of the research focused on the spatial dimensions of the informal economy and a typology of activities in this sector comprising home-based activities, itinerant informal economy workers, and sedentary commercial & artisanal activities located outside the home. Then the research presents a set of correlative elements between informal sector activities and housing system, the most important of which is housing and its surroundings, sites allocated for housing, The spatial distribution of the commercial activities, public space, mobility and transportation, social interaction, and up to the main actors in the housing stocks. The second part of the research is the analytical study of the above elements on Ezbet Khairallah and Othman housing "before and after Residents alterations". A comparative analysis has shown that where the planning system has failed to provide for the space needs of informal economic activities, operators have eventually found ways of meeting this need, often in spaces where such activities are not permitted. The research ends with the dynamic relationship between the informal sector activities and the housing system, also the importance of learning from informality in spatial planning, the need to adopt an integrated development approach and complement measures needed to effectively address the space needs of informal economy businesses in the urban development process.
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