A minimum cost spanning tree game is called ultrametric if the cost function on the edges of the underlying network is an ultrametric. We show that every ultrametric minimum cost spanning tree game is reduced to a cost allocation game on a rooted tree. It follows that there exist O(n) time algorithms for computing the Shapley value, the nucleolus and the egalitarian allocation of the ultrametri...

We show that the treewidth and the minimum fill-in of an n-vertex graph can be computed in time O(1.8899). Our results are based on combinatorial proofs that an n-vertex graph has O(1.7087) minimal separators and O(1.8135) potential maximal cliques. We also show that for the class of AT-free graphs the running time of our algorithms can be reduced to O(1.4142).

We present the first fully dynamic algorithm for maintaining a minimum spanning forest in time o( √ n) per operation. To be precise, the algorithm uses O(n1/3 logn) amortized time per update operation. The algorithm is fairly simple and deterministic. An immediate consequence is the first fully dynamic deterministic algorithm for maintaining connectivity and bipartiteness in amortized time O(n1...

We study Euclidean embeddings of Euclidean metrics and present the following four results: (1) an O(log n √ log logn) approximation for minimum bandwidth in conjunction with a semi-definite relaxation, (2) an O(log n) approximation in O(n) time using a new constraint set, (3) a lower bound of Θ( √ logn) on the least possible volume distortion for Euclidean metrics, (4) a new embedding with O( √...

K e y w o r d s Minimum forearm vascular resistance, Essential hypertension, Antihypertensive therapy, Ca antagonists, ACE inhibitor

We solve a problem posed by Ronald Graham about the minimum number, over all 2-colorings of [1, n], of monochromatic (x, y, x + ay) triples, a ≥ 2. We show that the minimum number of such triples is n 2 2a(a+2a+3) + O(n). We also find a new upper bound for the minimum number, over all r-colorings of [1, n], of monochromatic Schur triples, for r ≥ 3.

Given an instance of the minimum cost flow problem, a version of the corresponding inverse problem, called the capacity inverse problem, is to modify the upper and lower bounds on arc flows as little as possible so that a given feasible flow becomes optimal to the modified minimum cost flow problem. The modifications can be measured by different distances. In this article, we consider the capac...

In this study, an artificial neural network was used to predict the minimum force required to single point incremental forming (SPIF) of thin sheets of Aluminium AA3003-O and calamine brass Cu67Zn33 alloy. Accordingly, the parameters for processing, i.e., step depth, the feed rate of the tool, spindle speed, wall angle, thickness of metal sheets and type of material were selected as input and t...

Given a complete graph on n nodes with metric edge costs, the minimum-cost khop spanning tree (kHMST) problem asks for a spanning tree of minimum total cost such that the longest root-leaf-path in the tree has at most k edges. We present an algorithm that computes such a tree of total expected cost O(log n) times that of a minimum-cost k-hop spanning-tree.