40 is a near branch, an analogous argument again shows that Pin(b) is q's lower-right quadrant. Thus, q is the closest connection between p, Pin(a) and Pin(b). Except for redundancies and pruning of sub-optimal trees, BB-SORT-C searches over all possible ways to construct a Steiner tree sequentially, such that each sink is added by a closest connection to some edge in the current tree. Thus, we...

We introduce a family of sequential contributions rules for minimum cost spanning tree problems. Each member of the family assigns an agent some part of his immediate connection cost and all of his followers are equally responsible for the remaining part. We characterize the family by imposing the axioms of efficiency, non-negativity, independence of following costs, group independence, and wea...

Connection matrices for graph parameters with values in a field have been introduced by M. Freedman, L. Lovász and A. Schrijver (2007). Graph parameters with connection matrices of finite rank can be computed in polynomial time on graph classes of bounded tree-width. We introduce join matrices, a generalization of connection matrices, and allow graph parameters to take values in the tropical ri...

Civil engineers operate with such notions as tree–structured cost frames and graph–structured project plans. We show how a cost frame denotes a possibly infinite set of project plans and, vice–versa, how a project plan denotes a possibly infinite set of cost frames. The civil engineer, we claim, operates freely in a domain where cost frames determine project plans, namely the project plans whic...

plane and mulberry trees play a crucial role in purifying the polluted air in tehran as a majorcity. in this research, 13 main districts of tehran city were chosen as study area. 20 completely healthy planeand mulberry species were selected in similar ecological conditions and age range. the uptake of cd and pbwas determined using spectrophotometry, whereas the chlorophyll content was measured ...

The decision tree model has gained great popularity both in academia and industry due to its capability of learning highly non-linear decision boundaries, and at the same time, still preserving interpretability that usually translates into transparency of decision-making. However, it has been a longstanding challenge for learning robust decision tree models since the learning process is usually...

We define a D2CS of a graph G to be a set S ⊆ V (G) with diam(G[S]) ≤ 2. A D2CS arises in connection with conditional coloring and radio-k-coloring of graphs. We study the problem of counting and enumerating D2CS of a graph. We first prove the following propositions: (1) Let f (k, h) be the number of D2CS of a complete k-ary tree of height h. Then f (k, h) = k k−1 (f (k + 1, 1) − 4)(k h−1 − 1) ...

This paper presents a delay-bounded minimum Steiner tree algorithm. The delay bounds, given as inputs to the algorithm, can be diierent for each individual source-sink connection. The approach is based on feasible search optimization that satisses the delay bounds rst, then improves the routing tree for the cost minimization. Iterative cut-and-link tree transformation constrained by delay bound...

A proper geometric model of the vascular systems in the liver is crucial for modeling blood flow, the connection between the organ and the rest of the organism. In vivo imaging does not provide sufficient details, so an algorithmic concept for extending measured vascular tree data is needed such that geometrically realistic structures can be generated. We develop a quantification of similarity ...

This paper presents new single-layer, i.e., planarembeddable, clock tree constructions with exact zero skew under either the linear or the Elmore delay model. Our method, called Planar-DME, consists of two parts. The first algorithm, called Linear-Planar-DME, guarantees an optimal planar zero-skew clock tree (ZST) under the linear delay model. The second algorithm, called Elmore-Planar-DME, use...