Svante Carlsson

Small forwarding tables for fast routing lookups

For some time, the networking community has assumed that it is impossible to do IP routing lookups in software fast enough to support gigabit speeds. IP routing lookups must find the routing entry with the longest matching prefix, a task that has been thought to require hardware support at lookup frequencies of millions per second.We present a forwarding table data structure designed for quick routing lookups. Forwarding tables are small enough to fit in the cache of a conventional general purpose processor. With the table in cache, a 200 MHz Pentium Pro or a 333 MHz Alpha 21164 can perform a few million lookups per second. This means that it is feasible to do a full routing lookup for each IP packet at gigabit speeds without special hardware.The forwarding tables are very small, a large routing table with 40,000 routing entries can be compacted to a forwarding table of 150-160 Kbytes. A lookup typically requires less than 100 instructions on an Alpha, using eight memory references accessing a total of 14 bytes.

Online Routing in Convex Subdivisions

We consider online routing algorithms for finding paths between the vertices of plane graphs. We show (1) there exists a routing algorithm for arbitrary triangulations that has no memory and uses no randomization, (2) no equivalent result is possible for convex subdivisions, (3) there is no competitive online routing algorithm under the Euclidean distance metric in arbitrary triangulations, and (4) there is no competitive online routing algorithm under the link distance metric even when the input graph is restricted to be a Delaunay, greedy, or minimum-weight triangulation.

Resizable Arrays in Optimal Time and Space

We present simple, practical and efficient data structures for the fundamental problem of maintaining a resizable one-dimensional array, A[l..l + n - 1], of fixed-size elements, as elements are added to or removed from one or both ends. Our structures also support access to the element in position i. All operations are performed in constant time. The extra space (i.e., the space used past storing the n current elements) is O√n at any point in time. This is shown to be within a constant factor of optimal, even if there are no constraints on the time. If desired, each memory block can be made to have size 2k - c for a specified constant c, and hence the scheme works effectively with the buddy system. The data structures can be used to solve a variety of problems with optimal bounds on time and extra storage. These include stacks, queues, randomized queues, priority queues, and deques.

An implicit binomial queue with constant insertion time

We introduce a new representation of a priority queue in an array such that the operation of insert can be performed in constant time and minimum extraction in logarithmic time. In developing this structure we first introduce a very simple scheme permitting insertions in constant amortized time. This is modified to achieve the worst-case behavior using roughly lg*n pairs of pointers, and finally this pointer requirement is removed.

A variant of Heapsort with almost optimal number of comparisons

Abstract An algorithm, which asymptotically halves the number of comparisons made by the common Heapsort , is presented and analysed in the worst case. The number of comparisons is shown to be (n+1)(log(n+1)+log log(n+1)+1.82)+O(log n) in the worst case to sort n elements, without using any extra space. Quicksort , which usually is referred to as the fastest in-place sorting method, uses 1.38n log n − O(n) in the average case (see Gonnet (1984)).

The Deap—A double-ended heap to implement double-ended priority queues

Abstract This paper presents a symmetrical implicit double-ended priority queue implementation, which can be built in linear time. The smallest and the largest element can be found in constant time, and deleted in logarithmic time. This structure is an improvement of the MinMaxHeap presented by Atkinson et al. (1986).

Finding the shortest watchman route in a simple polygon

Abstract. We present the first polynomial time algorithm that finds the shortest route in a simple polygon such that all points of the polygon are visible from the route. This route is called the shortest watchman route, and we do not assume any restrictions on the route or on the simple polygon. Our algorithm runs in worst case O(n6) time, but it is adaptive, making it run faster on polygons with a simple structure.

OPTIMUM GUARD COVERS AND m-WATCHMEN ROUTES FOR RESTRICTED POLYGONS

A watchman, in the terminology of art galleries, is a mobile guard. We consider several watchman and guard problems for different classes of polygons. We introduce the notion of vision spans along ...

Sublinear merging and natural merge sort

The complexity of merging two sorted sequences into one is linear in the worst case as well as in the average case. There are, however, instances for which a sublinear number of comparisons is sufficient. We consider the problem of measuring and exploiting such instance easiness. The merging algorithm presented, Adaptmerge, is shown to adapt optimally to different kinds of measures of instance easiness. In the sorting problem the concept of instance easiness has received a lot of attention, and it is interpreted by a measure of presortedness. We apply Adaptmerge in the already adaptive sorting algorithm Natural Mergesort. The resulting algorithm, Adaptive Mergesort, optimally adapts to several, known and new, measures of presortedness. We also prove some interesting results concerning the relation between measures of presortedness proposed in the literature.

ONLINE ROUTING IN CONVEX SUBDIVISIONS

We consider online routing algorithms for finding paths between the vertices of plane graphs. We show (1) there exists a routing algorithm for arbitrary triangulations that has no memory and uses n...