We address the following problem: Given a simple polygon $P$ with $n$ vertices and two points $s$ and $t$ inside it, find a minimum link path between them such that a given target point $q$ is visible from at least one point on the path. The method is based on partitioning a portion of $P$ into a number of faces of equal link distance from a source point. This partitioning is essentially a shor...

First, we present a simple algorithm which, given a sorted sequence of node values, can build a binary search tree of minimum height in O(N) time. The algorithm works with sequences whose length is, a priori, unknown. Previous algorithms [1-3] required the number of elements to be known in advance. Although the produced trees are of minimum height, they are generally unbalanced. We then show ho...

We consider the problem of computing a minimum cycle basis of an undirected non-negative edge-weighted graph G with m edges and n vertices. In this problem, a {0, 1} incidence vector is associated with each cycle and the vector space over F2 generated by these vectors is the cycle space of G. A set of cycles is called a cycle basis of G if it forms a basis for its cycle space. A cycle basis whe...

The Minimum Reservation Rate Problem arises in distributed systems for handling digital audio and video data The problem is to nd the minimum rate at which data must be reserved on a shared storage system in order to provide continuous bu ered playback of a variable rate output schedule The problem is equivalent to the minimum output rate given input rates during various time periods nd the min...

The Minimum Fill-in problem is to decide if a graph can be triangulated by adding at most k edges. Kaplan, Shamir, and Tarjan [FOCS 1994] have shown that the problem is solvable in time O(2O(k) + knm) on graphs with n vertices and m edges and thus is fixed parameter tractable. Here, we give the first subexponential parameterized algorithm solving Minimum Fillin in time O(2O( √ k log k) + knm). ...

Consider an n-vertex planar graph G. We present an O(n)-time algorithm for computing an embedding of G with minimum distance from the external face. This bound improves on the best previous bound by an O(n log n) factor. As a side effect, our algorithm improves the bounds of several algorithms that require the computation of a minimum distance embedding.

We give an O(n logn) time algorithm for factoring a string into the minimum number of palindromic substrings. That is, given a string S[1..n], in O(n logn) time our algorithm returns the minimum number of palindromes S1, . . . , Sl such that S = S1 · · ·Sl.

We show that the minimum fill-in and the minimum interval graph completion of a d-trapezoid graph can be computed in time O(n). We also show that the treewidth and the pathwidth of a d-trapezoid graph can be computed by an O(n tw(G) ) time algorithm. For both algorithms, d is supposed to be a fixed positive integer and it is required that a suitable intersection model of the given d-trapezoid g...

Whether a rigid body limits maneuverability depends on how maneuverability is defined. By the current definition, the minimum radius of the turn, a rigid-bodied, spotted boxfish Ostracion meleagris approaches maximum maneuverability, i.e. it can spin around with minimum turning radii near zero. The radius of the minimum space required to turn is an alternative measure of maneuverability. By thi...

Given a set P of n points in the plane and a number k, we want to find a polygon ~ with vertices in P of minimum area that satisfies one of the following properties: (1) cK is a convex k-gon, (2) ~ is an empty convex k-gon, or (3) ~ is the convex hull of exactly k points of P. We give algorithms for solving each of these three problems in time O(kn3). The space complexity is O(n) for k = 4 and ...