. We conduct an extensive computational study of shortest paths algorithms, including some very recent algorithms. We also suggest new algorithms motivated by the experimental results and prove interesting theoretical results suggested by the experimental data. Our computational study is based on several natural problem classes which identify strengths and weaknesses of various algorithms. These problem classes and algorithm implementations form an environment for testing the performance of shortest paths algorithms. The interaction between the experimental evaluation of algorithm behavior and the theoretical analysis of algorithm performance plays an important role in our research. Andrew V. Goldberg was supported in part by ONR Young Investigator Award N00014-91-J-1855, NSF Presidential Young Investigator Grant CCR-8858097 with matching funds from AT&T, DEC, and 3M, and a grant from Powell Foundation. This work was done while Boris V. Cherkassky was visiting Stanford University Compu...

Creating freeform surfaces is a challenging task even with advanced geometric modeling systems. Laser range scanners offer a promising alternative for model acquisition—the 3D scanning of existing objects or clay maquettes. The problem of converting the dense point sets produced by laser scanners into useful geometric models is referred to as surface reconstruction. In this paper, we present a procedure for reconstructing a tensor product B-spline surface from a set of scanned 3D points. Unlike previous work which considers primarily the problem of fitting a single B-spline patch, our goal is to directly reconstruct a surface of arbitrary topological type. We must therefore define the surface as a network of B-spline patches. A key ingredient in our solution is a scheme for automatically constructing both a network of patches and a parametrization of the data points over these patches. In addition, we define the B-spline surface using a surface spline construction, and demonstrate that such an approach leads to an efficient procedure for fitting the surface while maintaining tangent plane continuity. We explore adaptive refinement of the patch network in order to satisfy user-specified error tolerances, and demonstrate our method on both synthetic and real data.

This paper presents algorithms for the assignment problem, the transportation problem, and the minimum-cost flow problem of operations research. The algorithms find a minimumcost solution, yet run in time close to the best-known bounds for the corresponding problems without costs. For example, the assignment problem (equivalently, minimum-cost matching in a bipartite graph) can be solved in O(v/’rn log(nN)) time, where n, m, and N denote the number of vertices, number of edges, and largest magnitude of a cost; costs are assumed to be integral. The algorithms work by scaling. As in the work of Goldberg and Tarjan, in each scaled problem an approximate optimum solution is found, rather than an exact optimum.

This paper describes critical implementation issues that must be addressed to develop a fully automatic inliner. These issues are: integration into a compiler, program representation, hazard prevention, expansion sequence control, and program modi cation. An automatic inter- le inliner that uses pro le information has been implemented and integrated into an optimizing C compiler. The experimental results show that this inliner achieves signi cant speedups for production C programs.

The algorithms described in this thesis are designed to schedule cells in a very high-speed, parallel, input-queued crossbar switch. We present several novel scheduling algorithms that we have devised, each aims to match the set of inputs of an input-queued switch to the set of outputs more efficiently, fairly and quickly than existing techniques. In Chapter 2 we present the simplest and fastest of these algorithms: SLIP --- a parallel algorithm that uses rotating priority ("round-robin") arbitration. SLIP is simple: it is readily implemented in hardware and can operate at high speed. SLIP has high performance: for uniform i.i.d. Bernoulli arrivals, SLIP is stable for any admissible load, because the arbiters tend to desynchronize. We present analytical results to model this behavior. However, SLIP is not always stable and is not always monotonic: adding more traffic can actually make the algorithm operate more efficiently. We present an approximate analytical model of this behavior. SLIP prevents starvation: all contending inputs are eventually served. We present simulation results, indicating SLIP's performance. We argue that SLIP can be readily implemented for a 32x32 switch on a single chip. In Chapter 3 we present i-SLIP, an iterative algorithm that improves upon SLIP by converging on a maximal size match. The performance of i-SLIP improves with up to log 2 N iterations. We show that although it has a longer running time than SLIP, an i-SLIP scheduler is little more complex to implement. In Chapter 4 we describe maximum or maximal weight matching algorithms based on the occupancy of queues, or waiting times of cells. These algorithms are stabl...

This paper describes a method for generating test sequences for checking the conformance of a protocol implementation to its specification. A Rural Chinese Postman Tour is used to determine a minimum-cost tour of the transition graph of a finite-state machine. When used in combination with Unique Input/Output Sequences [18], the technique yields an efficient method for computing a test sequence for protocol conformance testing.

We present a randomized linear-time algorithm to find a minimum spanning tree in a connected graph with edge weights. The algorithm uses random sampling in combination with a recently discovered linear-time algorithm for verifying a minimum spanning tree. Our computational model is a unit-cost random-access machine with the restriction that the only operations allowed on edge weights are binary comparisons.

Efficient implementations of Dijkstra’s shortest path algorithm are investigated. A new data structure, called the radix heap, is proposed for use in this algorithm. On a network with n vertices, m edges, and nonnegative integer arc costs bounded by C, a one-level form of radix heap gives a time bound for Dijkstra’s algorithm of O(m + n log C). A two-level form of radix heap gives a bound of O(m + n log C/log log C). A combination of a radix heap and a previously known data structure called a Fibonacci heap gives a bound of O(m + nm). The best previously known bounds are O(m + n log n) using Fibonacci heaps alone and O(m log log C) using the priority queue structure of Van Emde Boas et al. [17].

The watershed transform is the method of choice for image segmentation in the field of mathematical morphology. We present a critical review of several definitions of the watershed transform and the associated sequential algorithms, and discuss various issues which often cause confusion in the literature. The need to distinguish between definition, algorithm specification and algorithm implementation is pointed out. Various examples are given which illustrate di#erences between watershed transforms based on di#erent definitions and/or implementations. The second part of the paper surveys approaches for parallel implementation of sequential watershed algorithms.

Pajek is a program, for Windows, for analysis and visualization of large networks having some ten or houndred of thousands of vertices. In Slovenian language pajek means spider.