Among the properties of homogeneity of incidence structures flagtransitivity obviously is a particularly important and natural one. Consequently, in the last decades flag-transitive Steiner t-designs (i.e. flag-transitive t-(v, k, 1) designs) have been investigated, whereas only by the use of the classification of the finite simple groups has it been possible in recent years to essentially char...

The Covering Steiner problem is a common generalization of the k-MST and Group Steiner problems. An instance of the Covering Steiner problem consists of an undirected graph with edge-costs, and some subsets of vertices called groups, with each group being equipped with a non-negative integer value (called its requirement); the problem is to find a minimum-cost tree which spans at least the requ...

We study two-stage robust variants of combinatorial optimization problems like Steiner tree, Steiner forest, and uncapacitated facility location. The robust optimization problems, previously studied by Dhamdhere et al. [9], Golovin et al. [15], and Feige et al. [13], are two-stage planning problems in which the requirements are revealed after some decisions are taken in stage one. One has to th...

A Steiner 2-design S(2,k,v) is said to be halvable if the block set can be partitioned into two isomorphic sets. This is equivalent to an edge-disjoint decomposition of a self-complementary graph G on v vertices into Kks. The obvious necessary condition of those orders v for which there exists a halvable S(2,k,v) is that v admits the existence of an S(2,k,v) with an even number of blocks. In th...

Each strongly minimal Steiner k-system (M, R) (where is R a ternary collinearity relation) can be ‘coordinatized’ in the sense of (Ganter–Werner 1975) by quasigroup if k prime-power. We show this coordinatization never definable and k-systems constructed (Baldwin–Paolini 2020) interpret quasigroup. Nevertheless, refining construction, prime power, each (2, k)-variety quasigroups (Definition 3.1...

When relating a set of sequences by a phylogeny, we are essentially constructing a Steiner tree connecting the sequences in the space of all finite sequences. Finding an optimal Steiner tree is in most formulations hard, so population genetics and phylogenetics have often used spanning trees as an approximation for computational expediency. In this assessment you will be asked to investigate an...

In communication networks, many applications, such as video on demand and video conferencing, must establish a communications tree that spans a subset K in a vertex set. The source node can then send identical data to all nodes in set K along this tree. This kind of communication is known as multicast communication. A network optimization problem, called the Steiner tree problem (STP), is prese...

one of the most critical issues in designing Wireless Sensor Network (WSN) is to minimize the energy consumption. In Wireless Sensor Networks, data aggregation reduces the redundancy among sensed data and optimal sensor routing algorithm provides strategy for data gathering with minimum energy. The energy consumption is reduced by combining data fusion and cluster based routing. In this paper, ...