Exact exponential-time algorithms for NP-hard problems is an emerging field, and an increasing number of new results are being added continuously. Two important NP-hard problems that have been studied for decades are the treewidth and the minimum fill problems. Recently, an exact algorithm was presented by Fomin, Kratsch, and Todinca to solve both of these problems in time O∗(1.9601n). Their al...

We consider the problem of maintaining a set of n integers in the range 0::2 w ? 1 under the operations of insertion, deletion, predecessor queries, minimum queries and maximum queries on a unit cost RAM with word size w bits. Let f (n) be an arbitrary nondecreasing smooth function satisfying log log n f (n) p log n. A data structure is presented supporting insertions and deletions in worst cas...

Wedesign fast exponential time algorithms for some intractable graph-theoretic problems. Ourmain result states that aminimum optional dominating set in a graph of order n can be found in time O∗(1.8899n). Ourmethods to obtain this result involvematching techniques. The list of the considered problems includes Minimum Maximal Matching, 3Colourability, Minimum Dominating Edge Set, Minimum Connect...

We show that, using the L 1 metric, the minimum Hausdor distance under translation between two point sets of cardinality n in d-dimensional space can be computed in time O(n (4d 2)=3 log 2 n) for 3 < d 8, and in time O(n 5d=4 log 2 n) for any d > 8. Thus we improve the previous time bound of O(n 2d 2 log 2 n) due to Chew and Kedem. For d = 3 we obtain a better result of O(n 3 log 2 n) time by e...

We give faster approximation algorithms for the generalization of two NP-hard spanning tree problems. First, we investigate the problem of minimizing the degree of minimum spanning forests. Fischer [4] has shown how to compute a minimum spanning tree of degree at most b · ∆ + dlogb ne in time O(n 4+1/ ln ) for any b > 1, where ∆ is the value of an optimal solution. We model our generalization a...

The effect of incremental exercise to exhaustion on the change in pulmonary clearance rate (k) of aerosolized (99m)Tc-labeled diethylenetriaminepentaacetic acid ((99m)Tc-DTPA) and the relationship between k and arterial PO(2) (Pa(O(2))) during heavy work were investigated. Ten male cyclists (age = 25 +/- 2 yr, height = 180.9 +/- 4.0 cm, mass = 80.1 +/- 9.5 kg, maximal O(2) uptake = 5. 25 +/- 0....

In this paper we study the problem of computing subgraphs of a certain configuration in a given topological graph G such that the number of crossings in the subgraph is minimum. The configurations that we consider are spanning trees, s–t paths, cycles, matchings, and κ-factors for κ ∈ {1, 2}. We show that it is NP-hard to approximate the minimum number of crossings for these configurations with...

Given a graph with edge costs, the power of a node is the maximum cost of an edge incident to it, and the power of a graph is the sum of the powers of its nodes. Motivated by applications in wireless networks, we consider the following fundamental problem in wireless network design. Given a graph G = (V,E) with edge costs and degree bounds {r(v) : v ∈ V }, the Minimum-Power Edge-Multi-Cover (MP...

We introduce a technique using linear programming that may be used to analyse the worst-case performance of a class of greedy heuristics for certain optimisation problems on regular graphs. We demonstrate the use of this technique on heuristics for bounding the size of a minimum maximal matching (MMM), a minimum connected dominating set (MCDS) and a minimum independent dominating set (MIDS) in ...

We consider the problem of finding minimum-link rectilinear paths in rectilinear polygonal domains in the plane. A path or a polygon is rectilinear if all its edges are axis-parallel. Given a set P of h pairwise-disjoint rectilinear polygonal obstacles with a total of n vertices in the plane, a minimumlink rectilinear path between two points is a rectilinear path that avoids all obstacles with ...