a b s t r a c tWe place our focus on the gap between treewidth's success in producing fixed-parameter polynomial algorithms for hard graph problems, and specifically Hamiltonian Circuit and Max Cut, and the failure of its directed variants (directed treewidth (Johnson et al., 2001 [13]), DAG-width (Obdrzálek, 2006 [14]) and Kelly-width (Hunter and Kreutzer, 2007 [15]) to replicate it in the realm of digraphs. We answer the question of why this gap exists by giving two hardness results: we show that Directed Hamiltonian Circuit is W [2]-hard when the parameter is the width of the input graph, for any of these widths, and that Max Di Cut remains NP-hard even when restricted to DAGs, which have the minimum possible width under all these definitions. Along the way, we extend our reduction for Directed Hamiltonian Circuit to show that the related Minimum Leaf Outbranching problem is also W [2]-hard when naturally parameterized by the number of leaves of the solution, even if the input graph has constant width. All our results also apply to directed pathwidth and cycle rank.

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Residing in a country like Greece, where the earthquake is a common phenomenon in most of its areas, the need for constructing earthquake resistant buildings that will provide security and functionality to their residents is imperative. For this reason, the present study estimates the cost of constructing the same five-storey building in three different seismic hazard zones. Initially, this building is studied, in accordance with the provisions of Eurocode 8, for seismic zones I, II and III. The dimensioning and calculation of the weight of the required steel and the volume of the required concrete is carried out. The results from the three seismic zones are presented in detail, both for each structural element of the construction separately and for the whole construction, and a comparison is made between them.