Greg N. Frederickson and Ravi Janardan. Ecient message routing in planar networks. SIAM J. Comput., 18(4):843-857, 1989.  Home/Search   Document Not in Database   Summary   Related Articles   Check

.... King and Rossignac [KR99, Ros99] gave a triangulation compressor that guarantees 3:67 bits per node, the best possible rate being log 2 (256=27) 3:24 bits per node from Tutte s enumerative formula [Tut62] Routing table design for a network has been investigated in the case of planar networks [FJ89, GH99, Lu02a, Tho01] The underlying graph of the network is preprocessed in order to optimize routing tables, a data structure dedicated to each node in charge of nding the next output port given the destination address of an incoming message. The main objective is to minimize the size of the ....

Greg N. Frederickson and Ravi Janardan. Ecient message routing in planar networks. SIAM Journal on Computing, 18(4):843-857, August 1989.

.... Rossignac [KR99, Ros99] gave a triangulation compressor that guarantees 3:67 bits per node encoding, the best possible rate being log 2 (256=27) 3:24 bits per node from Tutte s enumerative formula [Tut62] Routing table design for a network has been investigated in the case of planar networks [FJ89, GH99, Lu02a, Tho01] The underlying graph of the network is pre processed in order to optimize routing tables. Such data structures are dedicated to each node in charge of nding the next output port given the destination address of an incoming message. The main objective is to minimize the size ....

Greg N. Frederickson and Ravi Janardan. Ecient message routing in planar networks. SIAM Journal on Computing, 18(4):843-857, August 1989.

....addresses and for routing tables (cf. Lei92] For non regular topologies and wider class of graphs, several trade o s between the stretch and the size of the routing tables have been achieved. In particular, for c decomposable graphs [FJ90] including bounded tree width graphs) planar graphs [FJ89, Lu02] and bounded pagenumber graphs and bounded genus graphs [GH99] More recently, a multiplicative 1 stretched routing scheme for every planar graph, for every 0, with only (log n) O(1) bit addresses and routing tables, has been announced in [Tho01] For more detailed presentation ....

Greg N. Frederickson and Ravi Janardan. Ecient message routing in planar networks. SIAM Journal on Computing, 18(4):843-857, August 1989.

....background concerning partitions of planar graphs. A region is a connected subgraph of a planar graph. One can distinguish two kinds of nodes: internal (belonging to only one region) and boundary nodes (that belong to two or more regions) The following decomposition lemma has been established in [FJ89] using the O( n) separator theorem, and used in the analysis of compact routing in planar graphs. Lemma 2.1 [FJ89] For every n node planar graph G and integer k 0, it is possible (in polynomial time) to partition the nodes of G into k regions, each of O(n=k) nodes and with n=k) boundary ....

....two kinds of nodes: internal (belonging to only one region) and boundary nodes (that belong to two or more regions) The following decomposition lemma has been established in [FJ89] using the O( n) separator theorem, and used in the analysis of compact routing in planar graphs. Lemma 2. 1 [FJ89] For every n node planar graph G and integer k 0, it is possible (in polynomial time) to partition the nodes of G into k regions, each of O(n=k) nodes and with n=k) boundary nodes, such that any path connecting an internal node of one region to an internal node of another must go through at ....

Greg N. Frederickson and Ravi Janardan. Ecient message routing in planar networks. SIAM Journal on Computing, 18(4):843-857, August 1989.

....and distances structure of planar graphs is probably dicult and certainly would require more combinatorics. Surprisingly, bounds for multiplicative stretched routing and approximated distance labeling are much more competitive. In general almost poly logarithmic space per node is sucient [FJ89, Tho01] Observe that shortest path and additive stretched routing in planar graphs are two equivalent problems in the sense that the lower bounds on the shortest path version transfer to lower bounds on stretched version by subdividing each edge by a constant . This forces any O( stretched ....

Greg N. Frederickson and Ravi Janardan. Ecient message routing in planar networks. SIAM Journal on Computing, 18(4):843-857, August 1989.

....Each routing table requires O(n) space in an n node network, which is not ecient (and even feasible) for large networks of computers. The methods to reduce the amount of space needed at each node have been intensively studied and there are many techniques to compress the size of routing tables [FJ88, FJ89, ABNLP90, TvL95]. The general idea is to group the destination addresses that correspond to the same outgoing link (at a node) and to encode the group so that it is easy to verify if a given destination address is in the group or not. A well known solution is to use intervals as groups of destination addresses. ....

Greg N. Frederickson and Ravi Janardan. Ecient message routing in planar networks. SIAM J. Comput., 18(4):843-857, 1989.

.... decomposition with a separator based divide and conquer technique due to Frederickson [21] Obviously all pairs shortest paths can be computed in time O(nm) after which the queries we describe can be answered in time O(1) but some faster algorithms are known for approximate planar shortest paths [23, 24, 31]. Our data structure answers shortest path queries exactly, in less preprocessing time than the other known results, but can only nd paths of constant length. A nal note of caution is in order. One should not be confused by the super cial similarity between the subgraph isomorphism problems ....

G. N. Frederickson and R. Janardan. Ecient message routing in planar networks. SIAM J. Computing 18:843-857, 1989.

....is an ecient allocation of memory compared to explicit routing schemes. Throughout this thesis, we consider only valid interval labeling schemes. It has been shown that an IRS can route messages on shortest paths on particular network topologies, such as trees, rings, hyper cubes, and others [SK85, vLT87, FJ89]. Unfortunately, this is not true in general networks; there are classes of networks which do not have any IRS which routes messages on shortest paths. Many schemes have been introduced in order to overcome this problem and to expand the classes of networks which support IRS with the desired ....

....destination address. Ideally, for general networks, we would like to have algorithms which are simple and which use a small amount of space to store the preprocessed information [TvL95, FGS93, NO99, Fre96] Such routing schemes are called compact routing schemes and have been studied extensively [FJ86, FJ88, FJ89, Cow99, KK96]. One example of such a routing scheme is a pre x routing scheme [TvL95] In this scheme, we label each node of the network with a string, over some alphabet , which serves as a name. We also label each link at a node with a unique string, possibly by , the empty string. When a message arrives ....

Greg N. Frederickson and Ravi Janardan. Ecient message routing in planar networks. SIAM J. Comput., 18(4):843-857, 1989.

....background concerning partitions of planar graphs. A region is a connected subgraph of a planar graph. One can distinguish two kinds of nodes: internal (belonging to only one region) and boundary nodes (that belong to two or more regions) The following decomposition lemma has been established in [FJ89] using the O( p n) separator theorem. Lemma 1. FJ89] For every n node planar graph G and integer k 0, it is possible (in polynomial time) to partition the nodes of G into k regions, each of O(n=k) nodes and with O( p n=k) boundary nodes, such that any path connecting an internal node of ....

....is a connected subgraph of a planar graph. One can distinguish two kinds of nodes: internal (belonging to only one region) and boundary nodes (that belong to two or more regions) The following decomposition lemma has been established in [FJ89] using the O( p n) separator theorem. Lemma 1. [FJ89] For every n node planar graph G and integer k 0, it is possible (in polynomial time) to partition the nodes of G into k regions, each of O(n=k) nodes and with O( p n=k) boundary nodes, such that any path connecting an internal node of one region to an internal node of another must go through ....

G. N. Frederickson and R. Janardan. Ecient message routing in planar networks. SIAM Journal on Computing, 18(4):843-857, Aug. 1989.

.... decomposition with a separator based divide and conquer technique due to Frederickson [21] Obviously all pairs shortest paths can be computed in time O(nm) after which the queries we describe can be answered in time O(1) but some faster algorithms are known for approximate planar shortest paths [23, 24, 31]. Our data structure answers shortest path queries exactly, in less preprocessing time than the other known results, but can only nd paths of constant length. A nal note of caution is in order. One should not be confused by the super cial similarity between the subgraph isomorphism problems ....

G. N. Frederickson and R. Janardan. Ecient message routing in planar networks. SIAM J. Computing 18:843-857, 1989.

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Greg N. Frederickson and Ravi Janardan. Ecient message routing in planar networks. SIAM J. Comput., 18(4):843-857, 1989.

No context found.

G. N. Frederickson and R. Janardan. Ecient message routing in planar networks. SIAM Journal on Computing, 18(4):843-857, 1989.

No context found.

G.N. Frederickson and R. Janardan. Ecient message routing in planar networks. SIAM Journal on Computing, 18:843-857, 1989.

No context found.

Greg N. Frederickson and Ravi Janardan. Ecient message routing in planar networks. SIAM Journal on Computing, 18(4):843-857, August 1989.

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G.N. Frederickson and R. Janardan, Ecient message routing in planar networks, SIAM Journal of Computing 19 (1990), 164-181.

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Greg N. Frederickson and Ravi Janardan. Ecient message routing in planar networks. SIAM Journal on Computing, 18(4):843-857, August 1989.

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G.N. Frederickson and R. Janardan. Ecient message routing in planar networks. SIAM J. on Computing, 18(4):843-857, August 1989.

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