Prompted by the advent of QoS routing in the Internet, we investigate the properties that path weight functions must have so that hop-by-hop routing is possible and optimal paths can be computed with a generalized Dijsktra's algorithm. For this purpose we define an algebra of weights which contains a binary operation, for the composition of link weights into path weights, and an order relation. Isotonicity is the key property of the algebra. It states that the order relation between the weights of any two paths is preserved if both of them are either prefixed or appended by a common, third, path. We show that isotonicity is both necessary and sufficient for a generalized Dijkstra's algorithm to yield optimal paths. Likewise, isotonicity is also both necessary and sufficient for hop-by-hop routing. However, without strict isotonicity, hop-by-hop routing based on optimal paths may produce routing loops. They are prevented if every node computes what we call lexicographic-optimal paths. These paths can be computed with an enhanced Dijkstra's algorithm that has the same complexity as the standard one. Our findings are extended to multipath routing as well. As special cases of the general approach, we conclude that shortestwidest paths can neither be computed with a generalized Dijkstra's algorithm nor can packets be routed hop-by-hop over those paths. In addition, loop-free hop-by-hop routing over widest and widest-shortest paths requires that each node computes lexicographic-optimal paths, in general.

Providing quality-of-service (QoS) guarantees in packet networks gives rise to several challenging issues. One of them is how to determine a feasible path that satisfies a set of constraints while maintaining high utilization of network resources. The latter objective implies the need to impose an additional optimality requirement on the feasibility problem. This can be done through a primary cost function (e.g., administrative weight, hop-count) according to which the selected feasible path is optimal. In general, multi-constrained path selection, with or without optimization, is an NP-complete problem that cannot be exactly solved in polynomial time. Heuristics and approximation algorithms with polynomialand pseudo-polynomial-time complexities are often used to deal with this problem. However, existing solutions suffer either from excessive computational complexities that cannot be used for online network operation or from low performance. Moreover, they only deal with special cases of the problem (e.g., two constraints without optimization, one constraint with optimization, etc.). For the feasibility problem under multiple constraints, some researchers have recently proposed a nonlinear cost function whose minimization provides a continuous spectrum of solutions ranging from a generalized linear approximation (GLA) to an asymptotically exact solution. In this paper, we propose an efficient heuristic algorithm for the most general form of the problem. We first formalize the theoretical properties of the above nonlinear cost function. We then introduce our heuristic algorithm (H MCOP), which attempts to minimize both the nonlinear cost function (for the feasibility part) and the primary cost function (for the optimality part). We prove that H MCOP guarantees at least t...

One of the key steps in Network-on-Chip (NoC) based design is spatial mapping of cores and routing of the communication between those cores. Known solutions to the mapping and routing problem first map cores onto a topology and then route communication, using separated and possibly conflicting objective functions. In this paper we present a unified single-objective algorithm, called Unified MApping, Routing and Slot allocation (UMARS). As the main contribution we show how to couple path selection, mapping of cores and TDMA time-slot allocation such that the network required to meet the constraints of the application is minimized. The time-complexity of UMARS is low and experimental results indicate a run-time only 20 % higher than that of path selection alone. We apply the algorithm to an MPEG decoder System-on-Chip (SoC), reducing area by 33%, power by 35% and worst-case latency by a factor four over a traditional multi-step approach.

Novel routing paradigms based on policies, quality of service (QoS) requirements, and packet content have been proposed for the Internet over the last decade. Constraint-based routing algorithms select a routing path satisfying constraints which are either administrativeoriented (policy routing), or service-oriented (QoS routing). The routes, in addition to satisfying constraints, are selected to reduce costs, balance network load, or increase security. In this paper, we discuss several constraint-based routing approaches and explain their requirements, complexity, and recent research proposals. In addition, we illustrate how these approaches can be integrated with Internet label switching and QoS architectures. We also discuss examples of application-level routing techniques used in today's Internet.

Various real-time services, like webcasting, audio/videoconferencing and telemedicine, are being deployed over the Internet. This requires the network to provide the guarantee of the service being provided to the receiver. The needs of the application is specified in terms of the Quality of Service (QoS) metrics like desired bandwidth, response time, etc. End-to-end QoS can be provided most efficiently when each layer of the protocol stack translates the application provided requirement into layer specific requirement and satisfies the same. Network layer has a critical role to play in the QoS provision process. It provides the desired QoS by considering the QoS metrics in the path selection process. The focus of this paper is on the QoS routing algorithms and protocols for unicast and multicast in the IPv4 based Internet that constrains or optimizes an individual or combination of metrics. The desired features of a router supporting QoS have been discussed in detail. QoS routing leads to an increase

In this paper, we consider the problem of resource reservation for networks. Current approaches for resource reservation in Integrated Service Networks adopt an all-or-nothing approach, where partially acquired resources must be released if resources are not available at all routers on the chosen path. Furthermore, under high load, endsystems must retry requests repeatedly leading to inefficient allocation and increased traffic. We propose a new approach called Deferred REServation (DRES) that substantially improves performance (reduces the overall flow rejection probability and increases link utilization) over the all-or-nothing reservation approach. Flow admissibility is increased by deferring requests at routers for a limited period of time until resources are available. Analytical and simulation results confirm the performance benefits of our approach.

Recent work on differentiated services in the Internet has defined new notions of QoS that apply to aggregates of traffic in networks with coarse spatial granularity. Most proposals for differentiated services involve traffic control algorithms for aggregate service levels, packet marking and policing, and preferential treatment of marked packets in the network core. The issue of routing for enhancing aggregate QoS has not received a lot of attention. This study investigates the potential benefit of using alternate routing strategies in support of differentiated services. We propose a traffic control scheme, called Simple Alternate Routing (SAR), wherein portions of marked packet flows can be assigned to alternate paths through a Service Provider Network (SPN) in response to congestion feedback information. The scheme is simple, requiring only minor changes to the SPN border routers so that alternately routed packets can be tunneled via conventional paths to an intermediate bo...

We study the Maximum Independent Set of Rectangles (MISR) problem: given a collection R of n axis-parallel rectangles, find a maximum-cardinality subset of disjoint rectangles. MISR is a special case of the classical Maximum Independent Set problem, where the input is restricted to intersection graphs of axis-parallel rectangles. Due to its many applications, ranging from map labeling to data mining, MISR has received a significant amount of attention from various research communities. Since the problem is NP-hard, the main focus has been on the design of approximation algorithms. Several groups of researches have independently suggested O(log n)-approximation algorithms for MISR, and this remained the best currently known approximation factor for the problem. The main result of our paper is an O(log log n)-approximation algorithm for MISR. Our algorithm combines existing approaches for solving special cases of the problem, in which the input set of rectangles is restricted to containing specific intersection types, with new insights into the combinatorial structure of sets of intersecting rectangles in the plane. We also consider a generalization of MISR to higher dimensions, where rectangles are replaced by d-dimensional hyper-rectangles. Our results for MISR imply an O((log n) d−2 log log n)-approximation algorithm for this problem, improving upon the best previously known O((log n) d−1)-approximation.

Abstract. A resource reservation scheme is an important mechanism of providing guaranteed QoS to applications. Today the only protocol that is standardized by IETF is the resource reservation protocol RSVP. Development of the next generation of signaling protocols is still open for research and development. We now propose SOS – a simple signaling protocol for guaranteed service connections. It overcomes poor scalability of RSVP and is simpler than existing proposals: Our protocol does not require per-flow soft states in core routers; it is robust and can handle losses of all types of signaling messages. Simple operations in the routers allow processing of 700 thousand messages per second. 1

As a result of perceived limitations of TCP/IP in supporting high throughput applications, significant efforts have recently been devoted to develop alternative architectures based on the concept of advance channel reservation. In this paper, we develop a polynomial-time algorithmic framework, called Graded Channel Reservation (GCR), to support the implementation of such architectures. This framework enables users to specify minimum bandwidth and duration requirements for their connections. Upon receiving a request, GCR returns the highest graded path, selected according to a general, multi-criteria optimization objective. In particular, if the optimization criterion is delay, we prove that GCR returns the earliest time available to establish the connection. Thereafter, we present a generalization of GCR, called GCRswitch, that is capable of supporting path switching throughout a connection. We present practical methods for minimizing or limiting the number of path switches. Through extensive simulations, we evaluate the performance of GCR and its variants under various topological settings and applications workload. Our results show that, for certain traffic parameters, optimized path selection combined with path switching can reduce the average delay of requests by an order of magnitude and increase the maximum sustainable load by as much as 50%.