ASSTRACT. In the all-pair shortest distance problem, one computes the matrix D = (du), where dq is the minimum weighted length of any path from vertex i to vertexj in a directed complete graph with a weight on each edge. In all the known algorithms, a shortest path p, ~ achieving di./is also implicitly computed. In fact, logs(f (n)) is an information-theoretic lower bound, wheref(n) is the total number of distinct patterns (Po) for n-vertex graphs. As f(n) potentially can be as large as 2&quot;:', it would appear possible that a nontrivial lower bound can be derived this way in the decision tree model. The characterization and enumeration of realizable patterns is studied, and it is shown thatf(n) < C &quot;~. Thus no lower bound greater than Cn 2 can be derived from this approach. It is proved as a corollary that the Triangular polyhedron T ~&quot;~, defined in E ¢~' ~ by d,j> 0 and the triangle inequalities d~j + dik> d,k, has at most C&quot; ' faces of all dimensions, thus resolving an open question in a similar information bound approach to the shortest distance problem.

Abstract—The underlying concepts of an exact QoS routing algorithm are explained. We show that these four concepts, namely 1) nonlinear definition of the path length; 2) a-shortest path approach; 3) nondominance; and 4) look-ahead, are fundamental building blocks of a multiconstrained routing algorithm. The main reasons to consider exact multiconstrained routing algorithms are as follows. First, the NP-complete behavior seems only to occur in specially constructed graphs, which are unlikely to occur in realistic communication networks. Second, there exist exact algorithms that are equally complex as heuristics in algorithmic structure and in running time on topologies that do not induce NP-complete behavior. Third, by simply restricting the number of paths explored during the path computation, the computational complexity can be decreased at the expense of possibly loosing exactness. The presented four concepts are incorporated in SAMCRA, a self-adaptive multiple constraints routing algorithm. Index Terms—Look-ahead, path dominance, QoS routing, shortest path.

During the last years, several speed-up techniques for Dijkstra’s algorithm have been published that maintain the correctness of the algorithm but reduce its running time for typical instances. They are usually based on a preprocessing that annotates the graph with additional information which can be used to prune or guide the search. Timetable information in public transport is a traditional application domain for such techniques. In this paper, we provide a condensed overview of new developments and extensions of classic results. Furthermore, we discuss how combinations of speed-up techniques can be realized to take advantage from different strategies.

Given an n-vertex, m-edge directed network G with real costs on the edges and a designated source vertex s, we give a new algorithm to compute shortest paths from s. Our algorithm is a simple deterministic one with O(n² log n) expected running time over a large class of input distributions. This is the first strongly polynomial algorithm in over 35 years to improve upon some aspect of the O(nm) running time of the Bellman-Ford algorithm. The result extends to an O(n² log n) expected running time algorithm for finding the minimum mean cycle, an improvement over Karp's O(nm) worst-case time bound when the underlying graph is dense. Both of our time bounds are shown to be achieved with high probability.

Network flow problems form a core area of Combinatorial Optimization. Their significance arises both from their very large number of applications and their theoretical importance. This thesis focuses on efficient exact algorithms for network flow problems in P and on approximation algorithms for NP -hard variants such as disjoint paths and unsplittable flow. Given an n-vertex

AND ITS APPLICATION TO BIOMEDICAL LITERATURE F. Lunin . . . . . . 47 I

This report describes the methodologies and procedures developed through a contract to the University of Texas at Austin, in collaboration with the University of Maryland, to address these essential needs. Specifically, a simulation-assignment methodology has been developed to describe user's path choices in the network in response to real-time information, and the resulting flow patterns that propagate through the network, yielding information about overall quality of service and effectiveness, as well as localized information pointing to problem spots and opportunities for improvement. This methodology is intended for use off-line for evaluation purposes, or on-line for prediction purpose in support of advanced traffic management functions. In additional, algorithmic procedures have been developed to determine the best paths to which users should be directed so as to optimize overall system performance. Powerful extension