This document proves the problem of finding a minimum cost Steiner Tree covering k terminals with at most p branching nodes (with outdegree greater than 1), in a directed or an undirected planar graph with n nodes, is hard to approximate within a better ratio than n, even when the parameter p is fixed. 1 Theorem Definition 1. In a undirected (resp. directed) tree, a branching node is a node who...

PURPOSE While a number of studies have evaluated the minimum number of axillary nodes that need to be examined to accurately determine nodal positivity or negativity, there is little information on the number of nodes which must be examined to determine the extent of nodal positivity. This study attempts to determine for patients with 1-3 positive nodes the probability that the number of positi...

background: the axillary and supraclavicular nodal volume treatment results in improvement of local control and survival after breast conserving surgery (bcs) or modified radical mastectomy (mrm). studies on the depth of these nodes have questioned the consistent use of standard fields for all patients. this study was done to assess the dose delivery to these lymph nodes with conventional treat...

Many appealing multicast services such as on-demand TV, teleconference, online games and etc. can benefit from high available bandwidth in multi-radio multi-channel wireless mesh networks. When multiple simultaneous transmissions use a similar channel to transmit data packets, network performance degrades to a large extant. Designing a good multicast tree to route data packets could enhance the...

Controlling large natural and technological networks is an outstanding challenge. It is typically neither feasible nor necessary to control the entire network, prompting us to explore target control: the efficient control of a preselected subset of nodes. We show that the structural controllability approach used for full control overestimates the minimum number of driver nodes needed for target...

Transport in weighted networks is dominated by the minimum spanning tree (MST), the tree connecting all nodes with the minimum total weight. We find that the MST can be partitioned into two distinct components, having significantly different transport properties, characterized by centrality--the number of times a node (or link) is used by transport paths. One component, superhighways, is the in...

nowadays, wireless sensor network has been of interest to investigators and the greatest challenge in this part is the limited energy of sensors. sensors usually are in the harsh environments and transit in these environments is hard and impossible and moreover the nodes use non- replaceable batteries. because of this, saving energy is very important. in this paper we tried to decrease hard and...

Given a set of nodes N (i 1, 2, ..., n) which may represent cities and a set of requirements ria which may represent the number of telephone calls between N and N j, the problem is to build a spanning tree connecting these n nodes such that the total cost of communication of the spanning tree is a minimum among all spanning trees. The cost of communication for a pair of nodes is r;a multiplied ...

In this paper, we describe a minimum spanning tree problem with variable degree bounds. The objective is to find a minimum cost spanning tree where the cost of each edge depends on the degree of its end nodes and where edges with a higher cost enable higher degrees. This problem is motivated by the design of wireless networks, where each wireless link, operating on a given frequency channel, mu...