The supremum, over all point sets, of the ratio between the length of the MST and the length of the Steiner tree is known as the Steiner ratio;6 it has been studied extensively in the last several years. A simple example (the three comers of an equilateral triangle) shows that the ...
Off-Canvas Navigation Menu ToggleContents sudsoln.x = round(sudsoln.x); y = ones(size(sudsoln.x));k = 2:9 y(:,:,k) = k;endS = sudsoln.x.*y;% multiply each entry by its depthS = sum(S,3);% S is 9-by-9 and holds the solved puzzledrawSudoku(S) ...
We consider now some other network optimization problems, in which the objective is to compute a shortest path, cycle, tree, or other graph, subject to various types of constraints. We focus primarily on two classes of problems: those of finding minimum-cost trees or tours that span some or...
Transportation and network designThe bi-objective minimum diameter-cost spanning tree problem (bi-MDCST) seeks spanning trees with minimum total cost and minimum diameter. The bi-objective version generalizes the well-known bounded diameter minimum spanning tree problem. The bi-MDCST is a NP-hard ...
options = optimoptions('fmincon','SpecifyObjectiveGradient',true,...'SpecifyConstraintGradient',true); problem.options = options; Currently, AD works only for first derivatives; it does not apply to second or higher derivatives. So, for example, if you want to use an analytic Hessian to speed...
The mcMST package for the R programming language contains several methods for solving the multi-criteria spanning tree problem (mcMST).Key features of the mcMST package are:A multi-objective version of Prim's algorithm. Evolutionary multi-objective algorithms (based on the Prüfer-encoding or ...
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This chapter focuses on the p-median problem (PMP) and its properties. We consider a pseudo-Boolean formulation of the PMP, demonstrate its advantages and derive the most compact MILP formulation for the PMP within the class of mixed-Boolean linear progr
where the inequalities g(x)≥b and x≥0 are the constraints that specify a convex polytope over which the objective function c(x) is to be minimized, and f is the finite set of feasible solutions x that satisfy the constraints. There are many real-life problems (e.g., vehicle routing...
For the tree-sparsity, the non-zeros cluster along the branches of the tree. That means, if a node is non-zero, then the other nodes that are on the branch from the root to the node are non-zeros. The tree-sparsity wildly exists in the wavelet coefficients of nature signals and ...