Tomio Hirata

A unified linear-time algorithm for computing distance maps

In this paper we give a simple unified algorithm for computing distance maps. The algorithm runs in O(N 2 ) time for an imput of N×N binary image.

AN INCREMENTAL ALGORITHM FOR CONSTRUCTING SHORTEST WATCHMAN ROUTES

The problem of finding the shortest watchman route in a simple polygon P through a point s on its boundary is considered. A route is a watchman route if every point inside P can be seen from at least one point along the route. We present an incremental algorithm that constructs the shortest watchman route in O(n3) time for a simple polygon with n edges. This improves the previous O(n4) bound.

CORRIGENDUM TO "AN INCREMENTAL ALGORITHM FOR CONSTRUCTING SHORTEST WATCHMAN ROUTES"

This corrigendum fixes an error that appears in the previously published papers concerning the watchman route problem. A modification to our incremental watchman route algorithm previously presented in this journal is made, which gives an O(n4) time solution to the watchman route problem.

Edge-deletion and edge-contraction problems

For a property -&-pgr; on graphs, the corresponding edge-deletion problem PED(-&-pgr;) (edge-contraction problem PEC(-&-pgr;), resp.) is defined as follows: Given a graph G, find a set of edges of minimum cardinality whose deletion (contraction, resp.) results in a graph satisfying property -&-pgr;. In this paper we show that the edge-deletion problem PED (-&-pgr;) (edge-contraction problem PEC (-&-pgr;), resp.) is NP-hard if -&-pgr; is hereditary on subgraphs (contractions, resp.) and is determined by the 3-connected components.

Approximation algorithms for the weighted independent set problem

In the unweighted case, approximation ratio for the independent set problem has been analyzed in terms of the graph parameters such as the number of vertices, maximum degree, and average degree. In the weighted case, no corresponding results are possible for average degree, since inserting the vertices with small weight decreases the average degree arbitrarily without significantly changing the approximation ratio. In this paper, we introduce weighted measures, namely “weighted” average degree and “weighted” inductiveness, and analyze algorithms for the weighted independent set problem in terms of these parameters.

Constructing Shortest Watchman Routes by Divide-and-Conquer

We study the problem of finding shortest watchman routes in simple polygons from which polygons are visible. We develop a divide-and-conquer algorithm that constructs the shortest watchman route in O(n2) time for a simple polygon with n edges. This improves the previous O(n3) bound [8] and confirms a conjecture due to Chin and Ntafos [4].

Approximation Algorithms for the Maximum Satisfiability Problem

The maximum satisfiability problem (MAX SAT) is: given a set of clauses with weights, find a truth assignment that maximizes the sum of the weights of the satisfied clauses. In this paper, we present approximation algorithms for MAX SAT, including a 0.76544-approximation algorithm. The previous best approximation algorithm for MAX SAT was proposed by Goemans-Williamson and has a performance guarantee of 0.7584. Our algorithms are based on semidefinite programming and the 0.75-approximation algorithms of Yannakakis and Goemans-Williamson.

Approximation algorithms for the weighted independent set problem in sparse graphs

The approximability of the unweighted independent set problem has been analyzed in terms of sparseness parameters such as the average degree and inductiveness. In the weighted case, no corresponding results are possible for average degree, since adding vertices of small weight can decrease the average degree arbitrarily without significantly changing the approximation ratio. In this paper, we introduce two weighted measures, namely weighted average degree and weighted inductiveness, and analyze algorithms for the weighted independent set problem in terms of these parameters.

Shortest Safari Routes in Simple Polygon

Let P be a simple polygon and let P be a collection of convex polygons that lie in the interior of P and are attached to the boundary of P. The safari rouit problem asks for a shortest route that visits each polygon in P. Let n be the total number of vertices of P and polygons in P. We first present an O(n2) time algorithm for the restricted case where the route is forced to pass through a starting point s on the boundary of P. This improves the previous O(mn2) result, where m is the cardinality of P and can be linear to n in the worst case. Using the algorithm for the restricted case, we further present an O(n2) time algorithm for the general case where the restriction of forcing the route through a specific point is removed.

A systolic algorithm for Euclidean distance transform

The Euclidean distance transform is one of the fundamental operations in image processing. It has been widely used in computer vision, pattern recognition, morphological filtering, and robotics. This paper proposes a systolic algorithm that computes the Euclidean distance map of an N times N binary image in 3N clocks on 2N2 processing cells. The algorithm is designed so that the hardware resources are reduced; especially no multipliers are used and, thus, it facilitates VLSI implementation