We present a new algorithm for finding minimum-link rec8 tilinear paths among rectilinear obstacles in the plane. The algorithm 9 runs in O(n+ h log h) time (after triangulation) and O(n) space, where 10 h is the number of obstacles and n is the total number of their vertices. 11 Further, for any point s, with the same time and space preprocessing as 12 above, given any query point t, we can co...

We give algorithms to find the optimal disjoint paths around a rectangle. The set of disjoint paths connects a set of sources to a set of sinks (no fixed pairing between the sources and sinks) on the boundary of a rectangle where either the longest path length or the total path length is minimized. One algorithm finds the set of disjoint paths with the longest path length minimized in O(n log n...

A clique-transversal of a graph G is a subset of vertices intersecting all the cliques of G. It is NP-hard to determine the minimum cardinality τc of a clique-transversal of G. In this work, first we propose an algorithm for determining this parameter for a general graph, which runs in polynomial time, for fixed τc. This algorithm is employed for finding the minimum cardinality clique-transvers...

Abst rac t . The minimum-redundancy prefix code problem is to determine a list of integer codeword lengths I = [li l i E {1.. . n}], given a list of n symbol weightsp = [pili C {1 .n}], such that ~'~ 2 -l ' < 1, 9 " i = l n and ~i=1 lipi is minimised. An extension is the minimum-redundancy length-limited prefix code problem, in which the further constraint li < L is imposed, for all i C {1. . ....

We present a factor 14D approximation algorithm for the minimum linear arrangement problem on series-parallel graphs, where D is the maximum degree in the graph. Given a suitable decomposition of the graph, our algorithm runs in time O(|E|) and is very easy to implement. Its divide-andconquer approach allows for an effective parallelization. Note that a suitable decomposition can also be comput...

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...

This work considers the (lowest) common ancestor problem in weighted directed acyclic graphs. The minimum-weight (lowest) common ancestor of two vertices is the vertex among the set of (lowest) common ancestors with the smallest ancestral distance. For the all-pairs minimum-weight common ancestor problem we present an O(nm) algorithm for arbitrary edge weights which is optimal for sparse graphs...

Assume that G(V; E) is a weighted, undirected, connected graph with n vertices. The k most vital edge problem with respect to a minimum spanning tree is to "nd a set S∗ of k edges from E such that the removal of the edges in S∗ results in the greatest increase in the weight of the minimum spanning tree in the resulting graph G(V; E−S∗). In this paper, an improved algorithm for the problem with ...

For an ordered sequence of n weights, Huuman's algorithm constructs in time and space O(n) a search tree with minimum average path length, or, which is equivalent, a minimum redundancy code. However, if an upper bound B is imposed on the length of the codewords, the best known algorithms for the construction of an optimal code have time and space complexities O(Bn 2). A new algorithm is present...

In this paper, we present the first correlated ab initio investigations on the ground electronic state of the O(2)-HF complex. Calculations were performed using the CCSD(T) method with the aug-cc-pVDZ and aug-cc-pVTZ basis sets. The results show that there are two equivalent minimum energy hydrogen-bonded structures of planar bent geometry, where the minima correspond to exchange of the oxygen ...