We present an approximation algorithm for the shortest descending path problem. Given a source s and a destination t on a terrain, a shortest descending path from s to t is a path of minimum Euclidean length on the terrain subject to the constraint that the height decreases monotonically as we traverse that path from s to t. Given any ε ∈ (0, 1), our algorithm returns in O(n log(n/ε)) time a de...

A path from s to t on a polyhedral terrain is descending if the height of a point p never increases while we move p along the path from s to t. No efficient algorithm is known to find a shortest descending path from s to t in a polyhedral terrain. We give some properties of such paths. In the case where the face sequence is specified, we show that the shortest descending path is unique, and giv...

We introduce the notion of a "short normal path" between matrices S and T, that is, a continuous path from S to T consisting of normal matrices and having the same length as the straight line path from S to T. By this means we prove that for certain normal matrices S and T the eigenvalues of S and T may be paired in such a way that the maximum distance (in the complex plane) between the pairs i...

A vertex dominating path in a graph is a path P such that every vertex outside P has a neighbor on P . In 1988 H. Broersma stated a result implying that every n-vertex kconnected graph G such that σ(k+2)(G) ≥ n− 2k − 1 contains a dominating path. We show that every n-vertex k-connected graph with σ2(G) ≥ 2n k+2 + f(k) contains a dominating path of length at most O(|T |), where T is a minimum do...

The Shortest Path Problem with Resource Constraints is a common subproblem in many Branch-Cut-and-Price algorithms (BCP), e.g., routing and scheduling problems. This paper presents a general label-setting algorithm for solving various shortest path problems. An integration of the ‘Shortest Path Problem with Resource Constraints and k-cycle elimination’ with the ‘Partial Elementarity’ is introdu...

a r t i c l e i n f o a b s t r a c t The length-constrained heaviest path (LCHP) in a weighted tree T , where each edge is assigned a weight and a length, is the path P in T with maximum total path weight and total path length bounded by a given value B. This paper presents an O (n log n) time LCHP algorithm which utilizes a data structure constructed from the spine decomposition of the input ...

Let T be a tree in which every edge is associated with a real number. The sum of a path in T is the sum of the numbers associated with the edges of the path and its length is the number of the edges in it. For two positive integers L1 ≤ L2 and two real numbers S1 ≤ S2, a path is feasible if its length is between L1 and L2 and its sum is between S1 and S2. We address the problem: Given a tree T ...

We show that for every forest T the linear rank-width of T is equal to the path-width of T , and the linear clique-width of T equals the path-width of T plus two, provided that T contains a path of length three. It follows that both linear rank-width and linear clique-width of forests can be computed in linear time. Using our characterization of linear rank-width of forests, we determine the se...

Let T be a tree with n nodes, in which each edge is associated with a length and a weight. The density-constrained longest (heaviest) path problem is to find a path of T with maximum path length (weight) whose path density is bounded by an upper bound and a lower bound. The path density is the path weight divided by the path length. We show that both problems can be solved in optimal O(n logn) ...

the chadegan metamorphic complex is a wnw-ese- trending antiformal structure located in sanandaj-sirjan structural zone, iran.the inner core of the structure is made of orthogneiss, containing eclogitic lenses. schists and marbles lie structurally above theorthogneiss and crop out in the external limbs of the antiformal dome. two main deformational episodes have been documented in theschists an...