Quality-of-service provisioning in high speed networks : routing perspectives

The continuous growth in both commercial and public network traffic with various quality-of-service (QoS) requirements is calling for better service than the current Internet\u27s best effort mechanism. One of the challenging issues is to select feasible paths that satisfy the different requirements of various applications. This problem is known as QoS routing. In general, two issues are related to QoS routing: state distribution and routing strategy. Routing strategy is used to find a feasible path that meets the QoS requirements. State distribution addresses the issue of exchanging the state information throughout the network, and can be further divided into two sub-problems: when to update and how to disseminate the state information. In this dissertation, the issue of when to update link state information from the perspective of information theory is addressed. Based on the rate-distortion analysis, an efficient scheme, which outperforms the state of the art in terms of both protocol overhead and accuracy of link state information, is presented. Second, a reliable scheme is proposed so that, when a link is broken, link state information is still reachable to all network nodes as long as the network is connected. Meanwhile, the protocol overhead is low enough to be implemented in real networks. Third, QoS routing is NP-complete. Hence, tackling this problem requires heuristics. A common approach is to convert this problem into a shortest path or k-shortest path problem and solve it by using existing algorithms such as Bellman-Ford and Dijkstra algorithms. However, this approach suffers from either high computational complexity or low success ratio in finding the feasible paths. Hence, a new problem, All Hops k-shortest Path (AHKP), is introduced and investigated. Based on the solution to AHKP, an efficient self-adaptive routing algorithm is presented, which can guarantee in finding feasible paths with fairly low average computational complexity. One of its most distinguished properties is its progressive property, which is very useful in practice: it can self-adaptively minimize its computational complexity without sacrificing its performance. In addition, routing without considering the staleness of link state information may generate a significant percentage of false routing. Our proposed routing algorithm is capable of minimizing the impact of stale link state information without stochastic link state knowledge. Fourth, the computational complexities of existing s-approximation algorithms are linearly proportional to the adopted linear scaling factors. Therefore, two efficient algorithms are proposed for finding the optimal (the smallest) linear scaling factor such that the computational complexities are reduced. Finally, an efficient algorithm is proposed for finding the least hop(s) multiple additive constrained path for the purpose of saving network resources

Computing backup forwarding rules in Software-Defined Networks

The past century of telecommunications has shown that failures in networks are prevalent. Although much has been done to prevent failures, network nodes and links are bound to fail eventually. Failure recovery processes are therefore needed. Failure recovery is mainly influenced by (1) detection of the failure, and (2) circumvention of the detected failure. However, especially in SDNs where controllers recompute network state reactively, this leads to high delays. Hence, next to primary rules, backup rules should be installed in the switches to quickly detour traffic once a failure occurs. In this work, we propose algorithms for computing an all-to-all primary and backup network forwarding configuration that is capable of circumventing link and node failures. Omitting the high delay invoked by controller recomputation through preconfiguration, our proposal's recovery delay is close to the detection time which is significantly below the 50 ms rule of thumb. After initial recovery, we recompute network configuration to guarantee protection from future failures. Our algorithms use packet-labeling to guarantee correct and shortest detour forwarding. The algorithms and labeling technique allow packets to return to the primary path and are able to discriminate between link and node failures. The computational complexity of our solution is comparable to that of all-to-all-shortest paths computations. Our experimental evaluation on both real and generated networks shows that network configuration complexity highly decreases compared to classic disjoint paths computations. Finally, we provide a proof-of-concept OpenFlow controller in which our proposed configuration is implemented, demonstrating that it readily can be applied in production networks

A Survey of Shortest-Path Algorithms

A shortest-path algorithm finds a path containing the minimal cost between two vertices in a graph. A plethora of shortest-path algorithms is studied in the literature that span across multiple disciplines. This paper presents a survey of shortest-path algorithms based on a taxonomy that is introduced in the paper. One dimension of this taxonomy is the various flavors of the shortest-path problem. There is no one general algorithm that is capable of solving all variants of the shortest-path problem due to the space and time complexities associated with each algorithm. Other important dimensions of the taxonomy include whether the shortest-path algorithm operates over a static or a dynamic graph, whether the shortest-path algorithm produces exact or approximate answers, and whether the objective of the shortest-path algorithm is to achieve time-dependence or is to only be goal directed. This survey studies and classifies shortest-path algorithms according to the proposed taxonomy. The survey also presents the challenges and proposed solutions associated with each category in the taxonomy

Adapted and constrained Dijkstra for elastic optical networks

We present an optimal and efficient algorithm for finding a shortest path in an elastic optical network. The algorithm is an adaptation of the Dijkstra shortest path algorithm, where we take into account the spectrum continuity and contiguity constraints, and a limit on the path length. The adaptation redefines the node label in the Dijkstra algorithm, allows for revisiting nodes even at a higher cost for different slices, avoids loops, and prunes worse labels. The algorithm is generic and agnostic of a specific spectrum allocation policy, as it finds the largest set of available slices from which slices can be allocated in any way. We describe and motivate the algorithm design, and point to our freely-available implementation using the Boost Graph Library. We carried out 8100 simulation runs for large, random and realistic networks, and found that the probability of establishing a connection using the proposed algorithm can be even twice as large as the probability of establishing a connection using the edge-disjoint shortest paths, and the Yen K shortest paths.Comment: 20th International Conference on Optical Network Design and Modeling (ONDM), pp. 200-205, May 201

Charting the Complexity Landscape of Waypoint Routing

Modern computer networks support interesting new routing models in which traffic flows from a source s to a destination t can be flexibly steered through a sequence of waypoints, such as (hardware) middleboxes or (virtualized) network functions, to create innovative network services like service chains or segment routing. While the benefits and technological challenges of providing such routing models have been articulated and studied intensively over the last years, much less is known about the underlying algorithmic traffic routing problems. This paper shows that the waypoint routing problem features a deep combinatorial structure, and we establish interesting connections to several classic graph theoretical problems. We find that the difficulty of the waypoint routing problem depends on the specific setting, and chart a comprehensive landscape of the computational complexity. In particular, we derive several NP-hardness results, but we also demonstrate that exact polynomial-time algorithms exist for a wide range of practically relevant scenarios

Finding and evaluating community structure in networks

We propose and study a set of algorithms for discovering community structure in networks -- natural divisions of network nodes into densely connected subgroups. Our algorithms all share two definitive features: first, they involve iterative removal of edges from the network to split it into communities, the edges removed being identified using one of a number of possible "betweenness" measures, and second, these measures are, crucially, recalculated after each removal. We also propose a measure for the strength of the community structure found by our algorithms, which gives us an objective metric for choosing the number of communities into which a network should be divided. We demonstrate that our algorithms are highly effective at discovering community structure in both computer-generated and real-world network data, and show how they can be used to shed light on the sometimes dauntingly complex structure of networked systems.Comment: 16 pages, 13 figure

The Online Replacement Path Problem

We study a natural online variant of the replacement path problem. The \textit{replacement path problem} asks to find for a given graph $G = (V,E)$, two designated vertices $s,t\in V$ and a shortest $s$-$t$ path $P$ in $G$, a \textit{replacement path} $P_e$ for every edge $e$ on the path $P$. The replacement path $P_e$ is simply a shortest $s$-$t$ path in the graph, which avoids the \textit{failed} edge $e$. We adapt this problem to deal with the natural scenario, that the edge which failed is not known at the time of solution implementation. Instead, our problem assumes that the identity of the failed edge only becomes available when the routing mechanism tries to cross the edge. This situation is motivated by applications in distributed networks, where information about recent changes in the network is only stored locally, and fault-tolerant optimization, where an adversary tries to delay the discovery of the materialized scenario as much as possible. Consequently, we define the \textit{online replacement path problem}, which asks to find a nominal $s$-$t$ path $Q$ and detours $Q_e$ for every edge on the path $Q$, such that the worst-case arrival time at the destination is minimized. Our main contribution is a label setting algorithm, which solves the problem in undirected graphs in time $O(m \log n)$ and linear space for all sources and a single destination. We also present algorithms for extensions of the model to any bounded number of failed edges.Comment: 18 page

A context-based geoprocessing framework for optimizing meetup location of multiple moving objects along road networks

Given different types of constraints on human life, people must make decisions that satisfy social activity needs. Minimizing costs (i.e., distance, time, or money) associated with travel plays an important role in perceived and realized social quality of life. Identifying optimal interaction locations on road networks when there are multiple moving objects (MMO) with space-time constraints remains a challenge. In this research, we formalize the problem of finding dynamic ideal interaction locations for MMO as a spatial optimization model and introduce a context-based geoprocessing heuristic framework to address this problem. As a proof of concept, a case study involving identification of a meetup location for multiple people under traffic conditions is used to validate the proposed geoprocessing framework. Five heuristic methods with regard to efficient shortest-path search space have been tested. We find that the R* tree-based algorithm performs the best with high quality solutions and low computation time. This framework is implemented in a GIS environment to facilitate integration with external geographic contextual information, e.g., temporary road barriers, points of interest (POI), and real-time traffic information, when dynamically searching for ideal meetup sites. The proposed method can be applied in trip planning, carpooling services, collaborative interaction, and logistics management.Comment: 34 pages, 8 figure

Applications of graph algorithms in GIS

A

Comparison and validation of community structures in complex networks

The issue of partitioning a network into communities has attracted a great deal of attention recently. Most authors seem to equate this issue with the one of finding the maximum value of the modularity, as defined by Newman. Since the problem formulated this way is NP-hard, most effort has gone into the construction of search algorithms, and less to the question of other measures of community structures, similarities between various partitionings and the validation with respect to external information. Here we concentrate on a class of computer generated networks and on three well-studied real networks which constitute a bench-mark for network studies; the karate club, the US college football teams and a gene network of yeast. We utilize some standard ways of clustering data (originally not designed for finding community structures in networks) and show that these classical methods sometimes outperform the newer ones. We discuss various measures of the strength of the modular structure, and show by examples features and drawbacks. Further, we compare different partitions by applying some graph-theoretic concepts of distance, which indicate that one of the quality measures of the degree of modularity corresponds quite well with the distance from the true partition. Finally, we introduce a way to validate the partitionings with respect to external data when the nodes are classified but the network structure is unknown. This is here possible since we know everything of the computer generated networks, as well as the historical answer to how the karate club and the football teams are partitioned in reality. The partitioning of the gene network is validated by use of the Gene Ontology database, where we show that a community in general corresponds to a biological process.Comment: To appear in Physica A; 25 page