Abstract—Open Shortest Path First (OSPF) is the most commonly used intra-domain internet routing protocol. Traffic flow is routed along shortest paths, splitting flow at nodes where several outgoing links are on shortest paths to the destination. The weights of the links, and thereby the shortest path routes, can be changed by the network operator. The weights could be set proportional to their physical distances, but often the main goal is to avoid congestion, i.e. overloading of links, and the standard heuristic recommended by Cisco is to make the weight of a link inversely proportional to its capacity. Our starting point was a proposed AT&T WorldNet backbone with demands projected from previous measurements. The desire was to optimize the weight setting based on the projected demands. We showed that optimizing the weight settings for a given set of demands is NP-hard, so we resorted to a local search heuristic. Surprisingly it turned out that for the proposed AT&T WorldNet backbone, we found weight settings that performed

Finding the lowest-cost path through a graph is central to many problems, including route planning for a mobile robot. If arc costs change during the traverse, then the remainder of the path may need to be replanned. This is the case for a sensor-equipped mobile robot with imperfect information about its environment. As the robot acquires additional information via its sensors, it can revise its plan to reduce the total cost of the traverse. If the prior information is grossly incomplete, the robot may discover useful information in every piece of sensor data. During replanning, the robot must either wait for the new path to be computed or move in the wrong direction; therefore, rapid replanning is essential. The D* algorithm (Dynamic A*) plans optimal traverses in real-time by incrementally repairing paths to the robot's state as new information is discovered. This paper describes an extension to D* that focusses the repairs to significantly reduce the total time re...

To guarantee typesafe execution, Java and other strongly typed languages require bounds checking of array accesses. Because arraybounds checks may raise exceptions, they block code motion of instructions with side effects, thus preventing many useful code optimizations, such as partial redundancy elimination or instruction scheduling of memory operations. Furthermore, because it is not expressible at bytecode level, the elimination of bounds checks can only be performed at run time, after the bytecode program is loaded. Using existing powerful bounds-check optimizers at run time is not feasible, however, because they are too heavyweight for the dynamic compilation setting. ABCD is a light-weight algorithm for elimination of Array Bounds Checks on Demand. Its design emphasizes simplicity and efficiency. In essence, ABCD works by adding a few edges to the SSA value graph and performing a simple traversal of the graph. Despite its simplicity, ABCD is surprisingly powerful. On our benchma...

Mobile robots often operate in domains that are only incompletely known, for example, when they have to move from given start coordinates to given goal coordinates in unknown terrain. In this case, they need to be able to replan quickly as their knowledge of the terrain changes. Stentz ’ Focussed Dynamic A * is a heuristic search method that repeatedly determines a shortest path from the current robot coordinates to the goal coordinates while the robot moves along the path. It is able to replan one to two orders of magnitudes faster than planning from scratch since it modifies previous search results locally. Consequently, it has been extensively used in mobile robotics. In this article, we introduce an alternative to Focussed Dynamic A * that implements the same navigation strategy but is algorithmically different. Focussed Dynamic A * Lite is simple, easy to understand, easy to analyze and easy to extend, yet is more efficient than Focussed Dynamic A*. We believe that our results will make D*-like replanning methods even more popular and enable robotics researchers to adapt them to additional applications. 1

but often the main goal is to avoid congestion, i.e. overloading of links, and the standard heuristic recommended by Cisco (a major router vendor) is to make the weight of a link inversely proportional to its capacity. We study the problem of optimizing OSPF weights for a given a set of projected demands so as to avoid congestion. We show this problem is NP-hard and propose a local search heuristic to solve it. We also provide worst-case results about the performance of OSPF routing vs. an optimal multi-commodity flow routing. Our numerical experiments compare the results obtained with our local search heuristic to the optimal multi-commodity flow routing, as well as simple and commonly used heuristics for setting the weights. Experiments were done with a proposed nextgeneration AT&T WorldNet backbone as well as synthetic internetworks.

This paper presents the first fully dynamic algorithms for maintaining all-pairs shortest paths in digraphs with positive integer weights less than b. For approximate shortest paths with an error factor of (2 + ffl), for any positive constant ffl, the amortized update time is O(n 2 log 2 n= log log n); for an error factor of (1 + ffl) the amortized update time is O(n 2 log 3 (bn)=ffl 2 ). For exact shortest paths the amortized update time is O(n 2:5 p b log n). Query time for exact and approximate shortest distances is O(1); exact and approximate paths can be generated in time proportional to their lengths. Also presented is a fully dynamic transitive closure algorithm with update time O(n 2 log n) and query time O(1). The previously known fully dynamic transitive closure algorithm with fast query time has one-sided error and update time O(n 2:28 ). The algorithms use simple data structures, and are deterministic.

The OSPF and IS-IS routing protocols widely used in today's Internet compute a shortest path tree (SPT) from each router to other routers in a routing area. Many existing commercial routers recompute an SPT from scratch following changes in the link states of the network. Such recomputation of an entire SPT is inecient and may consume a considerable amount of CPU time. Moreover, as there may coexist multiple SPTs in a network with a set of given link states, recomputation from scratch causes frequent unnecessary changes in the topology of an existing SPT and may lead to routing instability. In this paper, we present new dynamic SPT algorithms that make use of the structure of the previously computed SPT. Besides efficiency, our algorithm design objective is to achieve routing stability by making minimum changes to the topology of an existing SPT (while maintaining shortest path property) when some link states in the network have changed. We establish an algorithmic framework that allows ...

Incremental search techniques find optimal solutions to series of similar search tasks much faster than is possible by solving each search task from scratch. While researchers have developed incremental versions of uninformed search methods, we develop an incremental version of A*.

Today the Internet offers a single path between end-systems even though it intrinsically has a large multiplicity of paths. This paper proposes an evolutionary architectural framework “BANANAS ” aimed at simplifying the introduction of multipath routing in the Internet. The framework starts with the observation that a path can be encoded as a short hash (“PathID”) of a sequence of globally known identifiers. The PathID therefore has global significance (unlike MPLS or ATM labels). This property allows multipath capable nodes to autonomously compute PathIDs in a partially upgraded network without requiring an explicit signaling protocol for path setup. We show that this framework allows the introduction of sophisticated explicit routing and multipath capabilities within the context of widely deployed connectionless routing protocols (e.g. OSPF, IS-IS, BGP) or overlay networks. We establish these characteristics through the development of PathID encoding and routecomputation schemes. The BANANAS framework also allows considerable flexibility in terms of architectural function placement and complexity management. To illustrate this feature, we develop an efficient variable-length hashing scheme that moves control-plane complexity and state overheads to network edges, allowing a very simple interior node design. All the schemes have been evaluated using both sizable SSFNet simulations and Linux/Zebra implementation evaluated on Utah’s Emulab testbed facility. 1.

We present the first fully dynamic algorithm for maintaining all pairs shortest paths in directed graphs with real-valued edge weights. Given a dynamic directed graph G such that each edge can assume at most S di#erent real values, we show how to support updates in O(n amortized time and queries in optimal worst-case time. No previous fully dynamic algorithm was known for this problem. In the special case where edge weights can only be increased, we give a randomized algorithm with one-sided error which supports updates faster in O(S We also show how to obtain query/update trade-o#s for this problem, by introducing two new families of algorithms. Algorithms in the first family achieve an update bound of O(n/k), and improve over the best known update bounds for k in the . Algorithms in the second family achieve an update bound of ), and are competitive with the best known update bounds (first family included) for k in the range (n/S) # Work partially supported by the IST Programme of the EU under contract n. IST-199914. 186 (ALCOM-FT) and by CNR, the Italian National Research Council, under contract n. 01.00690.CT26. Portions of this work have been presented at the 42nd Annual Symp. on Foundations of Computer Science (FOCS 2001) [8] and at the 29th International Colloquium on Automata, Languages, and Programming (ICALP'02) [9].