Interval Routing Schemes for Circular-Arc Graphs

Interval routing is a space efficient method to realize a distributed routing function. In this paper we show that every circular-arc graph allows a shortest path strict 2-interval routing scheme, i.e., by introducing a global order on the vertices and assigning at most two (strict) intervals in this order to the ends of every edge allows to depict a routing function that implies exclusively shortest paths. Since circular-arc graphs do not allow shortest path 1-interval routing schemes in general, the result implies that the class of circular-arc graphs has strict compactness 2, which was a hitherto open question. Additionally, we show that the constructed 2-interval routing scheme is a 1-interval routing scheme with at most one additional interval assigned at each vertex and we an outline algorithm to calculate the routing scheme for circular-arc graphs in O(n^2) time, where n is the number of vertices.Comment: 17 pages, to appear in "International Journal of Foundations of Computer Science

The complexity of the characterization of networks supporting shortest-path interval routing

AbstractInterval Routing is a routing method that was proposed in order to reduce the size of the routing tables by using intervals and was extensively studied and implemented. Some variants of the original method were also defined and studied. The question of characterizing networks which support optimal (i.e., shortest path) Interval Routing has been thoroughly investigated for each of the variants and under different models, with only partial answers, both positive and negative, given so far. In this paper, we study the characterization problem under the most basic model (the one unit cost), and with the most restrictive memory requirements (one interval per edge). We prove that this problem is NP-hard (even for the restricted class of graphs of diameter at most 3). Our result holds for all variants of Interval Routing. It significantly extends some related NP-hardness result, and implies that, unless P=NP, partial characterization results of some classes of networks which support shortest path Interval Routing, cannot be pushed further to lead to efficient characterizations for these classes

SINGLE-ROW ROUTING PROBLEM WITH ALTERNATIVE TERMINALS

The present article concentrates on the dogleg-free Manhattan model where horizontal and vertical wire segments are positioned on different sides of the board and each net (wire) has at most one horizontal segment. Gallai's classical result on interval packing can be applied in VLS1 routing to find, in linear time, a minimum-width dogleg-free routing in the Manhattan model, provided that all the terminals are on one side of a rectangular (single-row routing). We deal with the generalization of this routing problem when we have the possibility to select another terminal from a corresponding set instead of a terminal to be connected. It will be shown that in this case there is no hope to find a polynomial algorithm because this problem is NP-complete. The results on dogleg-free Manhattan routing can be connected with other application areas related to colouring of interval graphs. In this paper the alternative interval placement problem will be defined. We show that this problem is NP-complete. This implies the NP-completeness of the single-row routing problem with alternative terminals

Self-stabilizing interval routing algorithm with low stretch factor

A compact routing scheme is a routing strategy which suggests routing tables that are space efficient compared to traditional all-pairs shortest path routing algorithms. An Interval Routing algorithm is a compact routing algorithm which uses a routing table at every node in which a set of destination addresses that use the same output port are grouped into intervals of consecutive addresses. Self-stabilization is a property by which a system is guaranteed to reach a legitimate state in a finite number of steps starting from any arbitrary state. A self-stabilizing Pivot Interval Routing (PIR) algorithm is proposed in this work. The PIR strategy allows routing along paths whose stretch factor is at most five, and whose average stretch factor is at most three with routing tables of size O(n3/2log 23/2n) bits in total, where n is the number of nodes in the network. Stretch factor is the maximum ratio taken over all source-destination pairs between the length of the paths computed by the routing algorithm and the distance between the source and the destination. PIR is also an Interval Routing Scheme (IRS) using at most 2n( 1+lnn)1/2 intervals per link for the weighted graphs and 3n(1+ lnn)1/2 intervals per link for the unweighted graphs. The preprocessing stage of the PIR algorithm consists of nodelabeling and arc-labeling functions. The nodelabeling function re-labels the nodes with unique integers so as to facilitate fewer number of intervals per arc. The arc-labeling is done in such a fashion that the message delivery protocol takes an optimal path if both the source and the destination are located within a particular range from each other and takes a near-optimal path if they are farther from each other

A multipopulation parallel genetic simulated annealing based QoS routing and wavelength assignment integration algorithm for multicast in optical networks

Copyright @ 2008 Elsevier B.V. All rights reserved.In this paper, we propose an integrated Quality of Service (QoS) routing algorithm for optical networks. Given a QoS multicast request and the delay interval specified by users, the proposed algorithm can find a flexible-QoS-based cost suboptimal routing tree. The algorithm first constructs the multicast tree based on the multipopulation parallel genetic simulated annealing algorithm, and then assigns wavelengths to the tree based on the wavelength graph. In the algorithm, routing and wavelength assignment are integrated into a single process. For routing, the objective is to find a cost suboptimal multicast tree. For wavelength assignment, the objective is to minimize the delay of the multicast tree, which is achieved by minimizing the number of wavelength conversion. Thus both the cost of multicast tree and the user QoS satisfaction degree can approach the optimal. Our algorithm also considers load balance. Simulation results show that the proposed algorithm is feasible and effective. We also discuss the practical realization mechanisms of the algorithm.This work was supported in part by the Engineering and Physical Sciences Research Council (EPSRC) of UK under Grant EP/E060722/1, the National Natural Science Foundation of China under Grant nos. 60673159 and 70671020, the National High-Tech Research and Development Plan of China under Grant no. 2006AA01Z214, Program for New Century Excellent Talents in University, and the Key Project of Chinese Ministry of Education under Grant no. 108040

An Evaluation of Controller and Pilot Performance, Workload and Acceptability under a NextGen Concept for Dynamic Weather Adapted Arrival Routing

In todays terminal operations, controller workload increases and throughput decreases when fixed standard terminal arrival routes (STARs) are impacted by storms. To circumvent this operational constraint, Prete, Krozel, Mitchell, Kim and Zou (2008) proposed to use automation to dynamically adapt arrival and departure routing based on weather predictions. The present study examined this proposal in the context of a NextGen trajectory-based operation concept, focusing on the acceptability and its effect on the controllers ability to manage traffic flows. Six controllers and twelve transport pilots participated in a human-in-the-loop simulation of arrival operations into Louisville International Airport with interval management requirements. Three types of routing structures were used: Static STARs (similar to current routing, which require the trajectories of individual aircraft to be modified to avoid the weather), Dynamic routing (automated adaptive routing around weather), and Dynamic Adjusted routing (automated adaptive routing around weather with aircraft entry time adjusted to account for differences in route length). Spacing Responsibility, whether responsibility for interval management resided with the controllers (as today), or resided with the pilot (who used a flight deck based automated spacing algorithm), was also manipulated. Dynamic routing as a whole was rated superior to static routing, especially by pilots, both in terms of workload reduction and flight path safety. A downside of using dynamic routing was that the paths flown in the dynamic conditions tended to be somewhat longer than the paths flown in the static condition

On the space requirement of interval routing

Interval routing is a space-efficient method for point-to-point networks. It is based on labeling the edges of a network with intervals of vertex numbers (called interval labels). An M-label scheme allows up to M labels to be attached on an edge. For arbitrary graphs of size n, n the number of vertices, the problem is to determine the minimum M necessary for achieving optimality in the length of the longest routing path. The longest routing path resulted from a labeling is an important indicator of the performance of any algorithm that runs on the network. We prove that there exists a graph with D = Ω(n1/3) such that if M ≤ n/18D - O(√n/D), the longest path is no shorter than D + Θ(D/√M). As a result, for any M-label IRS, if the longest path is to be shorter than D + Θ(D/√M), at least M = Ω(n/D) labels per edge would be necessary.published_or_final_versio

Let the Tree Bloom: Scalable Opportunistic Routing with ORPL

Routing in battery-operated wireless networks is challenging, posing a tradeoff between energy and latency. Previous work has shown that opportunistic routing can achieve low-latency data collection in duty-cycled networks. However, applications are now considered where nodes are not only periodic data sources, but rather addressable end points generating traffic with arbitrary patterns. We present ORPL, an opportunistic routing protocol that supports any-to-any, on-demand traffic. ORPL builds upon RPL, the standard protocol for low-power IPv6 networks. By combining RPL's tree-like topology with opportunistic routing, ORPL forwards data to any destination based on the mere knowledge of the nodes' sub-tree. We use bitmaps and Bloom filters to represent and propagate this information in a space-efficient way, making ORPL scale to large networks of addressable nodes. Our results in a 135-node testbed show that ORPL outperforms a number of state-of-the-art solutions including RPL and CTP, conciliating a sub-second latency and a sub-percent duty cycle. ORPL also increases robustness and scalability, addressing the whole network reliably through a 64-byte Bloom filter, where RPL needs kilobytes of routing tables for the same task

Self-Correcting Broadcast in Distributed Hash Tables

We present two broadcast algorithms that can be used on top of distributed hash tables (DHTs) to perform group communication and arbitrary queries. Unlike other P2P group communication mechanisms, which either embed extra information in the DHTs or use random overlay networks, our algorithms take advantage of the structured DHT overlay networks without maintaining additional information. The proposed algorithms do not send any redundant messages. Furthermore the two algorithms ensure 100% coverage of the nodes in the system even when routing information is outdated as a result of dynamism in the network. The first algorithm performs some correction of outdated routing table entries with a low cost of correction traffic. The second algorithm exploits the nature of the broadcasts to extensively update erroneous routing information at the cost of higher correction traffic. The algorithms are validated and evaluated in our stochastic distributed-algorithms simulator