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19
HighSpeed Policybased Packet Forwarding Using Efficient Multidimensional Range Matching
 In ACM SIGCOMM
, 1998
"... The ability to provide differentiated services to users with widely varying requirements is becoming increasingly important, and Internet Service Providers would like to provide these differentiated services using the same shared network infrastructure. The key mechanism, that enables differentiatio ..."
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Cited by 136 (0 self)
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The ability to provide differentiated services to users with widely varying requirements is becoming increasingly important, and Internet Service Providers would like to provide these differentiated services using the same shared network infrastructure. The key mechanism, that enables differentiation in a connectionless network, is the packet classification function that parses the headers of the packets, and after determining their context, classifies them based on administrative policies or realtime reservation decisions. Packet classification, however, is a complex operation that can become the bottleneck in routers that try to support gigabit link capacities. Hence, many proposals for differentiated services only require classification at lower speed edge routers and also avoid classification based on multiple fields in the packet header even if it might be advantageous to service providers. In this paper, we present new packet classification schemes that, with a worstcase and tr...
Beyond Best Effort: Router Architectures for the Differentiated Services of Tomorrow’s Internet
 IEEE Communications Magazine
, 1998
"... With the transformation of the Internet into a commercial infrastructure, the ability to provide differentiated services to users with widely varying requirements is rapidly becoming as important as meeting the massive increases in bandwidth demand. Hence, while deploying routers, switches, and tran ..."
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Cited by 69 (0 self)
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With the transformation of the Internet into a commercial infrastructure, the ability to provide differentiated services to users with widely varying requirements is rapidly becoming as important as meeting the massive increases in bandwidth demand. Hence, while deploying routers, switches, and transmission systems of ever increasing capacity, Internet service providers would also like to provide customerspecific differentiated services using the same shared network infrastructure. In this article, we describe router architectures that can support the two trends of rising bandwidth demand and rising demand for differentiated services. We focus on router mechanisms that can support differentiated services at a level not contemplated in proposals currently under consideration due to concern regarding their implementability at high speeds. We consider the types of differentiated services that service providers may want to offer and then discuss the mechanisms needed in routers to support them. We describe plausible implementations of these mechanisms (the scalability and performance of which have been demonstrated by implementation in a prototype system) and argue that it is
3D Vertical Ray Shooting and 2D Point Enclosure, Range Searching, and Arc Shooting Amidst Convex Fat Objects
 COMPUT. GEOM. THEORY APPL
, 1995
"... We present a new data structure for a set of n convex simplyshaped fat objects in the plane, and use it to obtain efficient and rather simple solutions to several problems including (i) vertical ray shooting  preprocess a set K of n nonintersecting convex simplyshaped flat objects in 3space, ..."
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Cited by 23 (4 self)
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We present a new data structure for a set of n convex simplyshaped fat objects in the plane, and use it to obtain efficient and rather simple solutions to several problems including (i) vertical ray shooting  preprocess a set K of n nonintersecting convex simplyshaped flat objects in 3space, whose xyprojections are fat, for efficient vertical ray shooting queries, (ii) point enclosure  preprocess a set C of n convex simplyshaped fat objects in the plane, so that the k objects containing a query point p can be reported efficiently, (iii) boundedsize range searching  preprocess a set C of n convex fat polygons, so that the k objects intersecting a `nottoolarge' query polygon can be reported efficiently, and (iv) boundedsize segment shooting  preprocess a set C as in (iii), so that the first object (if exists) hit by a `nottoolong' oriented query segment can be found efficiently. For the first three problems we construct data structures of size O(s (n) log 3 n)...
Scalable HighSpeed Prefix Matching
 ACM TRANSACTIONS ON COMPUTER SYSTEMS
, 2001
"... Finding the longest matching prefix from a database of keywords is an old problem with a number of applications, ranging from dictionary searches to advanced memory management to computational geometry. But perhaps today's most frequent best matching prefix lookups occur in the Internet, when forwar ..."
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Cited by 23 (4 self)
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Finding the longest matching prefix from a database of keywords is an old problem with a number of applications, ranging from dictionary searches to advanced memory management to computational geometry. But perhaps today's most frequent best matching prefix lookups occur in the Internet, when forwarding packets from router to router. Internet traffic volume and link speeds are rapidly increasing; at the same time, an increasing user population is increasing the size of routing tables against which packets must be matched. Both factors make router prefix matching extremely performance critical. In this paper, we introduce a taxonomy for prefix matching technologies, which we use as a basis for describing, categorizing, and comparing existing approaches. We then present in detail a fast scheme using binary search over hash tables, which is especially suited for matching long addresses, such as the 128 bit addresses proposed for use in the next generation Internet Protocol, IPv6. We also present optimizations that exploit the structure of existing databases to further improve access time and reduce storage space.
MultiMethod Dispatching: A Geometric Approach with Applications to String Matching Problems
, 1999
"... Current object oriented programming languages (OOPLs) rely on monomethod dispatching. Recent research has identified multimethods as a new, powerful feature to be added to OOPLs, and several experimental OOPLs now have multimethods. Their ultimate success and impact in practice depends, among ..."
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Cited by 15 (3 self)
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Current object oriented programming languages (OOPLs) rely on monomethod dispatching. Recent research has identified multimethods as a new, powerful feature to be added to OOPLs, and several experimental OOPLs now have multimethods. Their ultimate success and impact in practice depends, among other things, on whether multimethod dispatching can be supported efficiently. We show that the multimethod dispatching problem can be transformed to a geometric problem on multidimensional integer grids, for which we then develop a data structure that uses nearlinear space and has O(log log n) query time. This gives a solution whose performance almost matches that of the best known algorithm for standard monomethod dispatching. Our geometric data structure has other applications as well, namely in two string matching problems: matching multiple rectangular patterns against a rectangular query text, and approximate dictionary matching with edit distance at most one. Our results f...
Efficient Regular Data Structures and Algorithms for Dilation, Location and Proximity Problems
"... In this paper we investigate datastructures obtained by a recursive partitioning of the input domain into regions of equal size. One of the most well known examples of such a structure is the quadtree, used here as a basis for more complex data structures; we also provide multidimensional version ..."
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Cited by 14 (0 self)
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In this paper we investigate datastructures obtained by a recursive partitioning of the input domain into regions of equal size. One of the most well known examples of such a structure is the quadtree, used here as a basis for more complex data structures; we also provide multidimensional versions of the stratified tree by van Emde Boas [20]. We show that under the assumption that the input points have limited precision (i.e. are drawn from the integer grid of size u) these data structures yield efficient solutions to many important problems. In particular, they allow us to achieve O(log log u) time per operation for dynamic approximate nearest neighbor (under insertions and deletions) and exact online closest pair (under insertions only) in any constant dimension. They allow O(log log u) point location in a given planar shape or in its expansion (dilation by a ball of a given radius). Finally, we provide a linear time (optimal) algorithm for computing the expansion of a shape...
UNIFYING THE LANDSCAPE OF CELLPROBE LOWER BOUNDS
, 2008
"... We show that a large fraction of the datastructure lower bounds known today in fact follow by reduction from the communication complexity of lopsided (asymmetric) set disjointness. This includes lower bounds for: • highdimensional problems, where the goal is to show large space lower bounds. • co ..."
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Cited by 11 (0 self)
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We show that a large fraction of the datastructure lower bounds known today in fact follow by reduction from the communication complexity of lopsided (asymmetric) set disjointness. This includes lower bounds for: • highdimensional problems, where the goal is to show large space lower bounds. • constantdimensional geometric problems, where the goal is to bound the query time for space O(n·polylogn). • dynamic problems, where we are looking for a tradeoff between query and update time. (In this case, our bounds are slightly weaker than the originals, losing a lglgn factor.) Our reductions also imply the following new results: • an Ω(lgn/lglgn) bound for 4dimensional range reporting, given space O(n · polylogn). This is quite timely, since a recent result [39] solved 3D reporting in O(lg 2 lgn) time, raising the prospect that higher dimensions could also be easy. • a tight space lower bound for the partial match problem, for constant query time. • the first lower bound for reachability oracles. In the process, we prove optimal randomized lower bounds for lopsided set disjointness.
Delaunay Triangulations in O(sort(n)) Time and More
"... We present several results about Delaunay triangulations (DTs) and convex hulls in transdichotomous and hereditary settings: (i) the DT of a planar point set can be computed in expected time O(sort(n)) on a word RAM, where sort(n) is the time to sort n numbers. We assume that the word RAM supports ..."
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Cited by 8 (3 self)
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We present several results about Delaunay triangulations (DTs) and convex hulls in transdichotomous and hereditary settings: (i) the DT of a planar point set can be computed in expected time O(sort(n)) on a word RAM, where sort(n) is the time to sort n numbers. We assume that the word RAM supports the shuffleoperation in constant time; (ii) if we know the ordering of a planar point set in x and in ydirection, its DT can be found by a randomized algebraic computation tree of expected linear depth; (iii) given a universe U of points in the plane, we construct a data structure D for Delaunay queries: for any P ⊆ U, D can find the DT of P in time O(P  log log U); (iv) given a universe U of points in 3space in general convex position, there is a data structure D for convex hull queries: for any P ⊆ U, D can find the convex hull of P in time O(P (log log U) 2); (v) given a convex polytope in 3space with n vertices which are colored with χ> 2 colors, we can split it into the convex hulls of the individual color classes in time O(n(log log n) 2). The results (i)–(iii) generalize to higher dimensions. We need a wide range of techniques. Most prominently, we describe a reduction from DTs to nearestneighbor graphs that relies on a new variant of randomized incremental constructions using dependent sampling.
MultiDimensional Prefix Matching Using Line Search
, 2000
"... With the increasing popularity of firewalls, virtual private networks (VPNs) and Quality of Service (QoS) routing, packet classification becomes increasingly important in the Internet. The highperformance solutions known so far strongly rely on certain properties of the filter database to match aga ..."
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Cited by 7 (2 self)
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With the increasing popularity of firewalls, virtual private networks (VPNs) and Quality of Service (QoS) routing, packet classification becomes increasingly important in the Internet. The highperformance solutions known so far strongly rely on certain properties of the filter database to match against, such as a small number of distinct prefixes or the absence of conflicts. In this paper, we present Line Search as a twodimensional generalization of the onedimensional binary search on prefix lengths, exploiting the advantage given by the different approach therein. This algorithm also works best on the filter databases that are expected to occur most often, but degrades gracefully when these assumptions no longer hold. We also show how to efficiently extend the algorithm to a complete fivedimensional Internet Protocol (IP) and transport header match.
An optimaltime algorithm for shortest paths on a convex polytope in three dimensions
 IN PROC. 22ND ACM SYMPOS. COMPUT. GEOM
, 2006
"... We present an optimaltime algorithm for computing (an implicit representation of) the shortestpath map from a fixed source s on the surface of a convex polytope P in three dimensions. Our algorithm runs in O(n log n) time and requires O(n log n) space, where n is the number of edges of P. The algo ..."
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Cited by 7 (0 self)
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We present an optimaltime algorithm for computing (an implicit representation of) the shortestpath map from a fixed source s on the surface of a convex polytope P in three dimensions. Our algorithm runs in O(n log n) time and requires O(n log n) space, where n is the number of edges of P. The algorithm is based on the O(n log n) algorithm of Hershberger and Suri for shortest paths in the plane [22], and similarly follows the continuous Dijkstra paradigm, which propagates a “wavefront” from s along ∂P. This is effected by generalizing the concept of conforming subdivision of the free space used in [22], and by adapting it for the case of a convex polytope in R³, allowing the algorithm to accomplish the propagation in discrete steps, between the “transparent” edges of the subdivision. The algorithm constructs a dynamic version of Mount’s data structure [32] that implicitly encodes the shortest paths from s to all other points of the surface. This structure allows us to answer singlesource shortestpath queries, where the length of the path, as well as its combinatorial type, can be reported in O(log n) time; the actual path can be reported in additional O(k) time, where k is the number