allocating information carrier supplies such that certain end-to-end communication demands, as a collection of multicast sessions, are fulfilled. This formulation necessitates a cross-layer coupling. We aim at a computational characterization of the performance theoretically achievable with joint optimizations spanning the network stack.

We define general algebraic frameworks for shortest-distance problems based on the structure of semirings. We give a generic algorithm for finding single-source shortest distances in a weighted directed graph when the weights satisfy the conditions of our general semiring framework. The same algorithm can be used to solve efficiently classical shortest paths problems or to find the k-shortest distances in a directed graph. It can be used to solve single-source shortest-distance problems in weighted directed acyclic graphs over any semiring. We examine several semirings and describe some specific instances of our generic algorithms to illustrate their use and compare them with existing methods and algorithms. The proof of the soundness of all algorithms is given in detail, including their pseudocode and a full analysis of their running time complexity.

The max-flow min-cut theorem of Ford and Fulkerson is based on an even more foundational result, namely Menger's theorem on graph connectivity. Menger's theorem provides a good characterization for the following single-source disjoint paths problem: given a graph G, with a source vertex s and terminals t 1 , ..., t k , decide whether there exist edge-disjoint s-t i paths, for i = 1, ..., k. We consider a natural, NP-hard generalization of this problem, which we call the single-source unsplittable flow problem. We are given a source and terminals as before; but now each terminal t i has a demand ae i 1, and each edge e of G has a capacity c e 1. The problem is to decide whether one can choose a single s-t i path, for each i, so that the resulting set of paths respects the capacity constraints --- the total amount of demand routed across any edge e must be bounded by the capacity c e . The main results of this paper are constant-factor approximation algorithms for three n...

This paper presents a new algorithm for nding global min-cuts in weighted, undirected graphs. One of the strengths of the algorithm is its extreme simplicity. This randomized algorithm can be implemented as a strongly polynomial sequential algorithm with running time ~ O(mn 2), even if space is restricted to O(n), or can be parallelized as an RN C algorithm which runs in time O(log 2 n) on a CRCW PRAM with mn 2 log n processors. In addition to yielding the best known processor bounds on unweighted graphs, this algorithm provides the first proof that the min-cut problem for weighted undirected graphs is in RN C. The algorithm does more than find a single min-cut; it nds all of them. The algorithm also yields numerous results on network reliability, enumeration of cuts, multi-way cuts, and approximate min-cuts.

Authentication using a path of trusted intermediaries, each able to authenticate the next in the path, is a well-known technique for authenticating entities in a large-scale system. Recent work has extended this technique to include multiple paths in an effort to bolster authentication, but the success of this approach may be unclear in the face of intersecting paths, ambiguities in the meaning of certificates, and interdependencies in the use of different keys. Several authors have thus proposed metrics to evaluate the confidence afforded by a set of paths. In this paper we develop a set of guiding principles for the design of such metrics. We motivate our principles by showing how previous approaches fail with respect to them and what the consequences to authentication might be. We then propose a direction for constructing metrics that come closer to meeting our principles and thus, we believe, to being satisfactory metrics for authentication. 1 Introduction Determining the owner of...

We show that the minimum cut problem for weighted undirected graphs can be solved in NC using three separate and independently interesting results. The first is an (m 2 =n)-processor NC algorithm for finding a (2 + ffl)-approximation to the minimum cut. The second is a randomized reduction from the minimum cut problem to the problem of obtaining a (2 + ffl)-approximation to the minimum cut. This reduction involves a natural combinatorial Set-Isolation Problem that can be solved easily in RNC. The third result is a derandomization of this RNC solution that requires a combination of two widely used tools: pairwise independence and random walks on expanders. We believe that the set-isolation approach will prove useful in other derandomization problems. The techniques extend to two related problems: we describe NC algorithms finding minimum k-way cuts for any constant k and finding all cuts of value within any constant factor of the minimum. Another application of these techni...

Recently, several new algorithms have been developed for the minimum cut problem. These algorithms are very different from the earlier ones and from each other and substantially improve worst-case time bounds for the problem. We conduct experimental evaluation the relative performance of these algorithms. In the process, we develop heuristics and data structures that substantially improve practical performance of the algorithms. We also develop problem families for testing minimum cut algorithms. Our work leads to a better understanding of practical performance of the minimum cut algorithms and produces very efficient codes for the problem.

) Stavros G. Kolliopoulos 1 Clifford Stein 1 Abstract In the single-source unsplittable flow problem we are given a graph G; a source vertex s and a set of sinks t 1 ; : : : ; t k with associated demands. We seek a single s-t i flow path for each commodity i so that the demands are satisfied and the total flow routed across any edge e is bounded by its capacity c e : The problem is an NP-hard variant of max flow and a generalization of single-source edge-disjoint paths with applications to scheduling, load balancing and virtual-circuit routing problems. In a significant development, Kleinberg gave recently constant-factor approximation algorithms for several natural optimization versions of the problem [18]. In this paper we give a generic framework that yields simpler algorithms and significant improvements upon the constant factors. Our framework, with appropriate subroutines, applies to all optimization versions previously considered and treats in a unified manner directed and u...

A new measure of centrality, C,, is introduced. It is based on the concept of network flows. While conceptually similar to Freeman’s original measure, Ca, the new measure differs from the original in two important ways. First, C, is defined for both valued and non-valued graphs. This makes C, applicable to a wider variety of network datasets. Second, the computation of C, is not based on geodesic paths as is C, but on all the independent paths between all pairs of points in the network.

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