Stefano Pallottino

Directed hypergraphs and applications

This paper deals with directed hypergraphs as a tool to model and solve some calsses of problems arising in Operations Research and in Computer Science. Concepts such as connectivity, paths and cuts are defined. An extension of the amin duality results to a special class of hypergraphs is presented. Algorithms to perform visits of hypergraphs and to find optimal paths are studied in detail. Some applications arising in propositional logic, An-Or graphs, relational data bases and transportation analysis are presented. (A)

Equilibrium traffic assignment for large scale transit networks

Abstract This paper develops a graph-theoretic framework for large scale transit networks and provides new insight into the equilibrium traffic assignment methodology. Variational inequality formulations for the equilibrium traffic assignment are developed and algorithms for computing equilibrium flows are discussed. A new shortest hyperpaths problem is defined and computational techniques for shortest hyperpaths suggested.

A Modeling Framework for Passenger Assignment on a Transport Network with Timetables

This paper presents a new graph theoretic framework for the passenger assignment problem that encompasses simultaneously the departure time and the route choice. The implicit FIFO access to transit lines is taken into account by the concept of available capacity. This notion of flow priority has not been considered explicitly in previous models. A traffic equilibrium model is described and a computational procedure based on asymmetric boarding penalty functions is suggested.

Implicit Enumeration of Hyperpaths in a Logit Model for Transit Networks

This paper investigates the application of a logit model to urban transit networks where every set of competitive transit lines is described by a particular graph structure called hyperpath. It shows that a sequential form of the logit model transcends the inherent limitations of the global form while retaining the algorithmic advantages similar to those obtained with the ordinary logit model for private vehicle networks.

Circular shortest path in images

Abstract Shortest path algorithms have been used in a number of applications such as crack detection, road or linear feature extraction in images. There are applications where the starting and ending positions of the shortest path need to be constrained. In this paper, we present several new algorithms for the extraction of a circular shortest path in an image such that the starting and ending positions coincide. The new algorithms we developed include multiple search algorithm, image patching algorithm, multiple backtracking algorithm, the combination of image patching and multiple back-tracking algorithm, and approximate algorithm. The typical running time of our circular shortest path extraction algorithm on a 256×256 image is about 0.3 s on a rather slow 85 MHz Sun SPARC computer. A variety of real images for crack detection in borehole data and object boundary extraction have been tested and good results have been obtained.

Dynamic Shortest Paths Minimizing Travel Times and Costs

In this paper, we study dynamic shortest path problems, which is to determine a shortest path from a specified source node to every other node in the network where arc travel times change dynamically. We consider two problems: the minimum time walk problem (which is to find a walk with the minimum travel time) and the minimum cost walk problem (which is to find a walk with the minimum travel cost). The minimum time walk problem is known to be polynomially solvable for a class of networks called FIFO networks. This paper makes the following contributions: (i) we show that the minimum cost walk problem is an NP-complete problem; (ii) we develop a pseudopolynomial-time algorithm to solve the minimum cost walk problem (for integer travel times); and (iii) we develop a polynomial-time algorithm for the minimum time walk problem arising in road networks with traffic lights.

Route Choice on Transit Networks with Online Information at Stops

Passengers on a transit network with common lines are often faced with the problem of choosing between either to board the arriving bus or to wait for a faster one. Many assignment models are based on the classical assumption that at a given stop passengers board the first arriving carrier of a certain subset of the available lines, often referred to as the attractive set. In this case, it has been shown that, if the headway distributions are exponential, then an optimal subset of lines minimizing the passenger travel time can be easily determined. However, when online information on future arrivals of buses are posted at the stop, it is unlikely that the above classical assumption holds. In this case, passengers may choose to board a line that offers the best combination of displayed waiting time and expected travel time to their destination once boarded. In this paper, we propose a general framework for determining the probability of boarding each line available at a stop when online information on bus waiting times is provided to passengers. We will also show that the classical model without online information may be interpreted as a particular instance of the proposed framework, this way achieving an extension to general headway distributions. The impact of the availability of information regarding bus arrivals and that of the regularity of transit lines on the network loads, as well as on the passenger travel times, will be illustrated with small numerical examples.

Technical Note—Traffic Equilibrium Paradoxes

Paradoxes may occur when different traffic equilibrium models are applied starting from the same data. When in the traffic system “players” of different size are present, a Mixed Behavior Equilibrium can be stated. One should expect, by intuition, that total cost decreases with the reduction of noncooperative players on the network. This assumption does not hold in general. This paper provides numerical examples to show it. The problem of investigating the relationship between different equilibrium models arises when one considers a strategy for rerouting vehicles in road networks, in order to reduce congestion (Route Guidance Systems, for example). The importance of identifying paradoxical situations in such problems is briefly discussed.

Polynomial auction algorithms for shortest paths

In this paper we consider strongly polynomial variations of the auction algorithm for the single origin/many destinations shortest path problem. These variations are based on the idea of graph reduction, that is, deleting unnecessary arcs of the graph by using certain bounds naturally obtained in the course of the algorithm. We study the structure of the reduced graph and we exploit this structure to obtain algorithms withO (n min{m, n logn}) andO(n2) running time. Our computational experiments show that these algorithms outperform their closest competitors on randomly generated dense all destinations problems, and on a broad variety of few destination problems.

Fair dissections of spiders, worms, and caterpillars

In the present paper we deal with equipartition problems for special classes of trees, i. e., spiders, stars, worms, and caterpillars. We prove that the equipartition problem is NP-complete for spiders (and, hence, for general trees); on the other hand, we give efficient polynomial-time algorithms for stars, worms, and caterpillars.