Abstract. All previously known efftcient maximum-flow algorithms work by finding augmenting paths, either one path at a time (as in the original Ford and Fulkerson algorithm) or all shortest-length augmenting paths at once (using the layered network approach of Dinic). An alternative method based on the preflow concept of Karzanov is introduced. A preflow is like a flow, except that the total amount flowing into a vertex is allowed to exceed the total amount flowing out. The method maintains a preflow in the original network and pushes local flow excess toward the sink along what are estimated to be shortest paths. The algorithm and its analysis are simple and intuitive, yet the algorithm runs as fast as any other known method on dense. graphs, achieving an O(n)) time bound on an n-vertex graph. By incorporating the dynamic tree data structure of Sleator and Tarjan, we obtain a version of the algorithm running in O(nm log(n’/m)) time on an n-vertex, m-edge graph. This is as fast as any known method for any graph density and faster on graphs of moderate density. The algorithm also admits efticient distributed and parallel implementations. A parallel implementation running in O(n’log n) time using n processors and O(m) space is obtained. This time bound matches that of the Shiloach-Vishkin algorithm, which also uses n processors but requires O(n’) space.

The construction of disjoint paths in a network is a basic issue in combinatorial optimization: given a network, and specified pairs of nodes in it, we are interested in finding disjoint paths between as many of these pairs as possible. This leads to a variety of classical NP-complete problems for which very little is known from the point of view of approximation algorithms. It has recently been brought into focus in work on problems such as VLSI layout and routing in high-speed networks; in these settings, the current lack of understanding of the disjoint paths problem is often an obstacle to the design of practical heuristics.

Despite the decentralized and unorganized nature of the web, we show that the web self-organizes such that communities of highly related pages can be efficiently identified based purely on connectivity.

The primal-dual method is a standard tool in the design of algorithms for combinatorial optimization problems. This chapter shows how the primal-dual method can be modified to provide good approximation algorithms for a wide variety of NP-hard problems. We concentrate on results from recent research applying the primal-dual method to problems in network design.

Abstract. It is shown that the minimum cut ratio is within a factor of O(log k) of the maximum concurrent flow for k-commodity flow instances with arbitrary capacities and demands. This improves upon the previously best-known bound of O(log 2 k) and is existentially tight, up to a constant factor. An algorithm for finding a cut with ratio within a factor of O(log k) of the maximum concurrent flow, and thus of the optimal min-cut ratio, is presented.

Information theory has not yet had a direct impact on networking, although there are similarities in concepts and methodologies that have consistently attracted the attention of researchers from both fields. In this paper, we review several topics that are related to communication networks and that have an information theoretic flavor, including multiaccess protocols, timing channels, effective bandwidth of bursty data sources, deterministic constraints on datastreams, queueing theory, and switching networks. Keywords--- Communication networks, multiaccess, effective bandwidth, switching I. INTRODUCTION Information theory is the conscience of the theory of communication; it has defined the "playing field" within which communication systems can be studied and understood. It has provided the spawning grounds for the fields of coding, compression, encryption, detection, and modulation and it has enabled the design and evaluation of systems whose performance is pushing the limits of wha...

In this paper we show that, given a graph and parameters ffi and r, we can find either a Kr;r minor or an edge-cut of size O(mr=ffi) whose removal yields components of weak diameter O(r 2 ffi); i.e., every pair of nodes in such a component are at distance O(r 2 ffi) in the original graph. Using this lemma, we improve the best known bounds for the min-cut max-flow ratio for multicommodity flows in graphs with forbidden small minors. In general graphs, it was known that the ratio is O(log k) for the uniform-demand case (the case where there is a unit-demand commodity between every pair of nodes), and that the ratio is O(log 2 k) for arbitrary demands, where k is the number of commodities. In this paper we show that for graphs excluding any fixed graph as a minor (e.g. planar graphs or bounded-genus graphs), the ratio is O(1) for the uniform-demand case and O(log k) for the arbitrary demand case. For such graphs, our method yields min-ratio cut approximation algorithms wit...

Abstract. This paper presents a new approach to finding minimum cuts in undirected graphs. The fundamental principle is simple: the edges in a graph’s minimum cut form an extremely small fraction of the graph’s edges. Using this idea, we give a randomized, strongly polynomial algorithm that finds the minimum cut in an arbitrarily weighted undirected graph with high probability. The algorithm runs in O(n 2 log 3 n) time, a significant improvement over the previous Õ(mn) time bounds based on maximum flows. It is simple and intuitive and uses no complex data structures. Our algorithm can be parallelized to run in �� � with n 2 processors; this gives the first proof that the minimum cut problem can be solved in ���. The algorithm does more than find a single minimum cut; it finds all of them. With minor modifications, our algorithm solves two other problems of interest. Our algorithm finds all cuts with value within a multiplicative factor of � of the minimum cut’s in expected Õ(n 2 � ) time, or in �� � with n 2 � processors. The problem of finding a minimum multiway cut of a graph into r pieces is solved in expected Õ(n 2(r�1) ) time, or in �� � with n 2(r�1) processors. The “trace ” of the algorithm’s execution on these two problems forms a new compact data structure for representing all small cuts and all multiway cuts in a graph. This data structure can be efficiently transformed into the

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. Thus, several authors have 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 failed with respect to these priniciples and what the consequences to authentication might be. We then propose a new metric that appears to meet our principles, and so to be a satisfactory metric of authentication.

Abstract — The minimum energy required to transmit a bit of information through a network characterizes the most economical way to communicate in a network. In this paper, we show that under a layered model of wireless networks, the minimum energyper-bit for multicasting in a mobile ad hoc network can be found by a linear program; the minimum energy-per-bit can be attained by performing network coding. Compared with conventional routing solutions, network coding not only promises a potentially lower energy-per-bit, but also enables the optimal solution to be found in polynomial time, in sharp contrast with the NPhardness of constructing the minimum-energy multicast tree as the optimal routing solution. We further show that the minimum energy multicast formulation is equivalent to a cost minimization with linear edge-based pricing, where the edge prices are the energy-per-bits of the corresponding physical broadcast links. This paper also investigates minimum energy multicasting with routing. Due to the linearity of the pricing scheme, the minimum energy-per-bit for routing is achievable by using a single distribution tree. A characterization of the admissible rate region for routing with a single tree is presented. The minimum energy-per-bit for multicasting with routing is found by an integer linear program. We show that the relaxation of this integer linear program, studied earlier in the Steiner tree literature, can now be interpreted as the optimization for minimum energy multicasting with network coding. In short, this paper presents a unifying study of minimum energy multicasting with network coding and routing. Index Terms — Network coding, routing, multicast, Steiner tree, wireless ad hoc networks, energy efficiency, mobility.