We consider a class of network-design problems with minimum sum of modification and network costs for minimum spanning trees under Hamming distance. By constructing three auxiliary networks, we present a strongly polynomial-time algorithm for this problem. The method can be applied to solve many network-design problems. And, we show that a variation model of this problem is NP-hard, even when the underlying network is a tree, by transforming the 0–1 knapsack problem to this model.

The Nature Conservancy takes a strategic and systematic approach to conservation planning. Ecoregional assessments are used to set goals and identify geographical priorities, and Conservation Action Planning is used to develop strategic plans for conservation areas. This study demonstrates how these planning processes were applied at the seascape scale based on a case study of Kimbe Bay, Papua New Guinea. Conservation Action Planning was used to identify key threats and strategies, and systematic conservation planning (similar to that used for ecoregional assessments) was used to design a network of marine protected areas to be resilient to the threat of climate change. The design was based on an assessment of biodiversity and socio-economic values, and identified 14 Areas of Interest that meet specific conservation goals. A detailed community-based planning process is now underway with local communities that own and manage these areas to refine and implement the marine protected area network.

We present here a pricing model which is an extension of the cooperative game concept and which includes a notion of elastic demand. We present some existence results as well as an algorithm, and we conclude by discussing a specific problem related to network pricing.

Given a weighted undirected graph G = (V,E),a tree (respectively tour) cover of an edge-weighted graph is a set of edges which forms a tree (resp. closed walk) and covers every other edge in the graph. The tree (resp. tour) cover problem is of finding a minimum weight tree (resp. tour) cover of G. Arkin, Halldórsson and Hassin (1993) give approximation algorithms with factors respectively 3.5 and 5.5. Later Könemann, Konjevod, Parekh, and Sinha (2003) study the linear programming relaxations and improve both factors to 3. We describe in the first part of the paper a 2-approximation algorithm for the metric case of tree cover.In the second part, we will consider a generalized version of tree (resp. tour) covers problem which is to find a minimum tree (resp. tours) which covers a subset D ⊆ E of G.We show that the algorithms of Könemann et al.can be adapted for the generalized tree and tours covers problem with the same factors.

We study a continuous version of the capacity and flow assignment problem(CFA) where the design cost is combined with an average delay measureto yield a non convex objective function coupled with multicommodity flowconstraints. A separable convexification of each arc cost function is proposedto obtain approximate feasible solutions within easily computable gaps fromoptimality. On the other hand, DC (difference of convex functions) programming can be usedto compute accurate upper bounds and reduce the gap.The technique is shown to be effective when topology is assumedfixed and capacity expansion on some arcs is considered.

We present here models and algorithms for the construction of efficient path systems, robust to possible variations of the characteristics of the network. We propose some interpretations of these models and proceed to numerical experimentations of the related algorithms. We conclude with a discussion of the way those concepts may be applied to the design of a Public Transportation System.