Given a 2-node connected, undirected graph G = (V,E), with n nodes and m edges with real weights, and given a minimum spanning tree (MST) T = (V, ET ) of G, we study the problem of finding, for every node v ∈ V , the MST of G− v = (V \ {v}, E \ Ev), where Ev is the set of edges incident to v in G. We show that this problem can be solved in O(min(m ·α(n, n),m+ n log n)) time and O(m) space. Our ...

Rectangular p-centers of a nite planar point set P are the centers of at most p axis-parallel congruent squares of minimal size covering P . We give a simple linear time algorithm based on linear selection for the case p = 3. A linear algorithm for this problem is already known [7]. But it makes use of an LP -type [6] formulation of the problem with high combinatorial dimension (roughly 40) whi...

In this paper we study tracking performance limitation problems. Two issues are addressed, concerning how earlier results developed elsewhere may be extended to more general classes of reference signals, and how tracking performance may be further improved beyond that o ered by feedback control. Toward these issues we consider exponentially increasing reference inputs and examine the use of pre...

Abstract: In this paper, we show that adaptive controllers designed using the standard backstepping technique proposed in Krstic [1995] globally stabilize a class of uncertain systems with unknown input time delay and unmodeled dynamics. As such systems belong to nonminimum phase systems and thus our result extends the class of systems stabilizable from minimum phase systems when the standard b...

Current high-quality object detection approaches use the same scheme: salience-based object proposal methods followed by post-classification using deep convolutional features. This spurred recent research in improving object proposal methods [18, 32, 15, 11, 2]. However, domain agnostic proposal generation has the principal drawback that the proposals come unranked or with very weak ranking, ma...

We consider the problem of partitioning rectilinear polygons into rectangles, using segments of minimum total length. This problem is NP-hard for polygons with holes. Even for hole-free polygons no known algorithm can nd an optimal partitioning in less than O(n 4) time. We present the rst linear-time algorithm for computing rectangula-tions of hole-free polygons, within a constant factor of the...

This chapter addresses the problem of concurrent task and path planning for a number of surveillance Unmanned Ground Vehicles (UGVs) such that a user defined area of interest is covered by the UGVs’ sensors in minimum time. We first formulate the problem, and show that it is in fact a generalization of the Multiple Traveling Salesmen Problem (MTSP), which is known to be NP-hard. We then propose...

The minimum weighted completion time problem involves (i) a set J of n jobs, a positive weight wj for each job j ∈ J , and a release date rj before which it cannot be scheduled; (ii) a set of m machines, each of which can process at most one job at any time, and (iii) an arbitrary set of positive values {pi,j}, where pi,j denotes the time to process job j on machine i. A schedule involves assig...

The paper presents a dynamic solution method for dynamic minimum parametric networks flow. The solution method solves the problem for a special parametric dynamic network with linear lower bound functions of a single parameter. Instead directly work on the original network, the method implements a labelling algorithm in the parametric dynamic residual network and uses quickest paths from the so...

Two recent methods have increased hopes of finding a polynomial time solution to the problem of computing the minimum weight triangulation of a set S of n points in the plane . Both involve computing what was believed to be a connected or nearly connected subgraph of the minimum weight triangulation, and then completing the triangulation optimally. The first method uses the light graph of S as ...