A new video object segmentation algorithm, which utilizes an extension of recursive shortest spanning tree (RSST) algorithm, is introduced. A 2-D affine motion model is assumed, and correspondingly, for each region, the planar approximation for the given dense motion vector field is computed. Starting from each 2×2 block as a distinct region, the algorithm recursively searches for the best pair...

We give a necessary condition and a sufficient condition for a minimum-cost spanning tree game introduced by Bird to be submodular (or convex). When the cost is restricted to two values, we give a characterization of submodular minimum-cost spanning tree games. We also discuss algorithmic issues.

The Euclidean minimum spanning tree (EMST) is a fundamental and widely studied structure. In the approximate version we are given an n-element point set P in R and an error parameter ε > 0, and the objective is to compute a spanning tree over P whose weight is at most (1 + ε) times that of the true minimum spanning tree. Assuming that d is a fixed constant, existing algorithms have running time...

The prize-collecting generalized minimum spanning tree (PC-GMST) is defined as follows: Given an undirected graph G = (V, E), with node set V, edge set E, cost vector c ∈ R|E| + on the edges E, prize vector p ∈ R|V | + on the nodes V, and a set of K mutually exclusive and exhaustive node sets V1, ..., VK (i.e., V1 ⋂ Vj = ∅, if i 6= j, and Kk=1 Vk = V ), find a minimum cost tree spanning exactly...

This paper presents a toolbox for interactive image segmentation based on a series of nested partitions of increasing coarseness. The user can navigate among the different resolution levels and select regions with simple mouse clicks. The whole family of partitions can be created during a single morphological flooding of the image, leading to a very fast algorithm. The information is stored in ...

The Chile-UK quasar survey, a new-generation 140 deg UVX survey to B = 20, is now ∼ 25% complete. The catalogue currently contains 319 quasars and 93 emission line galaxies. Using the minimal-spanning tree method, we have independently confirmed the ∼ 200 h Mpc group of quasars at z ≃ 1.3 discovered by Clowes & Campusano (1991). We have discovered a new ∼ 150 h Mpc group of 13 quasars at median...

We investigate special cases of the quadratic minimum spanning tree problem (QMSTP) on a graph G = (V,E) that can be solved as a linear minimum spanning tree problem. Characterization of such problems on graphs with special properties are given. This include complete graphs, complete bipartite graphs, cactuses among others. Our characterization can be verified in O(|E|) time. In the case of com...

In direct interconnection networks, the collective communication operation one to all, which is usually referred to as broadcasting, can be generalized to allow one source node to send a message to a rectangular region of nodes, rather than to all nodes. Most of the proposed routing algorithms for direct mesh and torus networks use a broadcast tree of unicast messages. The minimum spanning tree...

In this paper, we propose three strategies for building a multicasting tree in a high-speed network. These strategies can be used in any network topology. The rst one is based on voting, the second based on constructing a minimum spanning tree, and the third based on repeatedly constructing multiple minimum spanning trees. To demonstrate the eeectiveness of these strategies, we show how to appl...

We show that the α-weight of an MST over n points in a metric space with upper box dimension d has a bound independent of n if α > d and does not have one if α < d.