Congestion Minimization for Multipath Routing via Multiroute Flows

Congestion minimization is a well-known routing problem for which there is an O(log n/loglog n)-approximation via randomized rounding due to Raghavan and Thompson. Srinivasan formally introduced the low-congestion multi-path routing problem as a generalization of the (single-path) congestion minimization problem. The goal is to route multiple disjoint paths for each pair, for the sake of fault tolerance. Srinivasan developed a dependent randomized scheme for a special case of the multi-path problem when the input consists of a given set of disjoint paths for each pair and the goal is to select a given subset of them. Subsequently Doerr gave a different dependentrounding scheme and derandomization. Doerr et al. considered the problem where the paths have to be chosen, and applied the dependent rounding technique and evaluated it experimentally. However, their algorithm does not maintain the required disjointness property without which the problem easily reduces to the standard congestion minimization problem. In this note we show a simple algorithm that solves the problem correctly without the need for dependent rounding --- standard independent rounding suffices. This is made possible via the notion of multiroute flows originally suggested by Kishimoto et al. One advantage of the simpler rounding is an improved bound on the congestion when the path lengths are short

Towards Duality of Multicommodity Multiroute Cuts and Flows: Multilevel Ball-Growing

An elementary h-route flow, for an integer h ≥ 1, is a set of h edge-disjoint paths between a source and a sink, each path carrying a unit of flow, and an h-route flow is a non-negative linear combination of elementary h-route flows. An h-route cut is a set of edges whose removal decreases the maximum h-route flow between a given source-sink pair (or between every source-sink pair in the multicommodity setting) to zero. The main result of this paper is an approximate duality theorem for multicommodity h-route cuts and flows, for h ≤ 3: The size of a minimum h-route cut is at least f/h and at most O(log 3 k·f) where f is the size of the maximum h-route flow and k is the number of commodities. The main step towards the proof of this duality is the design and analysis of a polynomial-time approximation algorithm for the minimum h-route cut problem for h = 3 that has an approximation ratio of O(log 3 k). Previously, polylogarithmic approximation was known only for h-route cuts for h ≤ 2. A key ingredient of our algorithm is a novel rounding technique that we call multilevel ball-growing. Though the proof of the duality relies on this algorithm, it is not a straightforward corollary of it as in the case of classical multicommodity flows and cuts. Similar results are shown also for the sparsest multiroute cut problem

Parametric min-cuts analysis in a network

AbstractThe all pairs minimum cuts problem in a capacitated undirected network is well known. Gomory and Hu showed that the all pairs minimum cuts are revealed by a min-cut tree that can be obtained by solving exactly (n−1) maximum flow problems, where n is the number of nodes in the network.In this paper we consider first the problem of finding parametric min-cuts for a specified pair of nodes when the capacity of an arc i is given by min{bi,λ}, where λ is the parameter, ranging from 0 to ∞. Next we seek the parametric min-cuts for all pairs of nodes, and achieve this by constructing min-cut trees for at most 2m different values of λ, where m is the number of edges in the network

MultiPaths Revisited - A novel approach using OpenFlow-enabled devices

This thesis presents novel approaches enhancing the performance of computer networks using multipaths. Our enhancements take the form of congestion- aware routing protocols. We present three protocols called MultiRoute, Step- Route, and finally PathRoute. Each of these protocols leverage both local and remote congestion statistics and build different representations (or views) of the network congestion by using an innovative representation of congestion for router-router links. These congestion statistics are then distributed via an aggregation protocol to other routers in the network. For many years, multipath routing protocols have only been used in simple situations, such as Link Aggregation and/or networks where paths of equal cost (and therefore equal delay) exist. But, paths of unequal costs are often discarded to the benefit of shortest path only routing because it is known that paths of unequal length present different delays and therefore cause out of order packets which cause catastrophic network performances. Further, multipaths become highly beneficial when alternative paths are selected based on the network congestion. But, no realistic solution has been proposed for congestion-aware multipath networks. We present in this thesis a method which selects alternative paths based on network congestion and completely avoids the issue of out of order packets by grouping packets into flows and binding them to a single path for a limited duration. The implementation of these protocols relies heavily on OpenFlow and NOX. OpenFlow enables network researchers to control the behavior of their network equipment by specifying rules in the routers flow table. NOX provides a simple Application Programming Interface (API) to program a routers flow table. Therefore by using OpenFlow and NOX, we are able to define new routing protocols like the ones which we will present in this thesis. We show in this thesis that grouping packets together, while not optimal, still provides a significant increase in network performance. More precisely we show that our protocols can, in some cases, achieve up to N times the throughput of Shortest Path (SP), where N is the number of distinct paths of identical throughput from source to destination. We also show that our protocols provide more predictable throughput than simple hash-based routing algorithms. Todays networks provide more and more connections between any source- destination pair. Most of these connections remain idle until some failure occurs. Using the protocols proposed in this thesis, networks could leverage the added bandwidth provided by these currently idle connections. Therefore, we could increase the overall performance of current networks without replacing the existing hardware

Research on the Multiroute Probit-Based Public Transit Assignment Model Based on Bus Stop

A public transit network differs from a general road network. The passenger flow of bus stops and the limited capacity of buses have a greater effect than road traffic flow on the running time of buses. As a result, conventional public transit assignment models that adopt the econometric road network path concept have numerous limitations. Based on the analysis, the generalized bus trip time chain is analyzed, and the concept of a congestion function is proposed to describe the relationship between trip resistance and flow in the current paper. On the premise of this study, the transit network resistance function is formed and the multiroute probit-based loading model is established. With using STOCH or Dial's algorithm, the process of distribution is proposed. Finally, the model is applied to the transit network assignment of Deqing Town in Zhejiang Province. The result indicates that the model can be applied to practical operations with high-precision results