Roberts, A., Symvonis, A., and Zhang, L. 1995. Routing on Trees via Matchings.  Home/Search   Document Details and Download   Summary   Related Articles   Check

....This problem was first defined and investigated in Alon et al. 1993, 1994] and an upper bound of 3(n Gamma 1) for the problem was obtained. The improvement of this upper bound to 13 5 n was obtained by a minor change in the algorithm combined with a more careful analysis of the algorithm Roberts et al. 1995]. Also in Roberts et al. 1995] upper bounds were derived for some special cases defined by the structure of the graphs: trees of bounded degree in 2n o(n) trees of degree at most 3 in 2n, and complete d ary trees in n o(n) In Hyer and Larsen [1996] the technical report version of the ....

....and investigated in Alon et al. 1993, 1994] and an upper bound of 3(n Gamma 1) for the problem was obtained. The improvement of this upper bound to 13 5 n was obtained by a minor change in the algorithm combined with a more careful analysis of the algorithm Roberts et al. 1995] Also in Roberts et al. 1995], upper bounds were derived for some special cases defined by the structure of the graphs: trees of bounded degree in 2n o(n) trees of degree at most 3 in 2n, and complete d ary trees in n o(n) In Hyer and Larsen [1996] the technical report version of the present paper, the upper bound ....

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Roberts, A., Symvonis, A., and Zhang, L. 1995. Routing on Trees via Matchings.

....initial con guration. This problem was rst de ned and investigated in [ACG93, ACG94] and an upper bound of 3(n 1) for the problem was obtained. The improvement of this upper bound to 13 5 n was obtained by a minor change in the algorithm combined with a more careful analysis of the algorithm [RSZ95b]. Also in [RSZ95b] upper bounds were derived for some special cases de ned by the structure of the graphs: trees of bounded degree in 2n o(n) trees of degree at most 3 in 2n, and complete d ary trees in n o(n) In [HL96] the technical report version of the present paper, the upper bound for ....

....This problem was rst de ned and investigated in [ACG93, ACG94] and an upper bound of 3(n 1) for the problem was obtained. The improvement of this upper bound to 13 5 n was obtained by a minor change in the algorithm combined with a more careful analysis of the algorithm [RSZ95b] Also in [RSZ95b], upper bounds were derived for some special cases de ned by the structure of the graphs: trees of bounded degree in 2n o(n) trees of degree at most 3 in 2n, and complete d ary trees in n o(n) In [HL96] the technical report version of the present paper, the upper bound for the general case ....

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Roberts, A., Symvonis, A., and Zhang, L. 1995. Routing on Trees via Matchings. In Lecture Notes of Computer Science, Vol. 955: 4th Workshop on Algorithms and Data Structures, 251 - 262.

....node satisfying proposition 1. Let h i denote the number of home packets in subtree T i . Then T i can be weakly heap ordered in at most h i steps if T i does not contain the green packet, and at most h i 1 steps otherwise. Proof Omitted. A proof of the lemma can be found in [HL96] and in [RSZ95a]. ut Weakly heap ordering of subtrees is one of the important subroutines of the algorithm to be presented in the next section; the other is cycles. Cycles are intended to be carried out after all subtrees have been weakly heap ordered. A cycle is a sequence of steps, the primary purpose of which ....

Roberts, A., Symvonis, A., and Zhang, L. 1995. Routing on Trees via Matchings. Technical Report 494, Basser Dept. of Computer Science, University of Sydney.

....defined and investigated in [1, 2] and an upper bound of 3(n Gamma 1) for the problem was obtained. As in later results, including the ones in our paper, routing is carried out separately for each tree in a spanning forest for the graph, The improvement of this upper bound to 13 5 n derived in [3] was obtained by a minor change in the algorithm combined with a more careful analysis of the algorithm. Also in [3] upper bounds were derived for some special cases defined by the structure of the graphs: trees of bounded degree in 2n o(n) trees of degree at most 3 in 2n, and complete d ary ....

....including the ones in our paper, routing is carried out separately for each tree in a spanning forest for the graph, The improvement of this upper bound to 13 5 n derived in [3] was obtained by a minor change in the algorithm combined with a more careful analysis of the algorithm. Also in [3], upper bounds were derived for some special cases defined by the structure of the graphs: trees of bounded degree in 2n o(n) trees of degree at most 3 in 2n, and complete d ary trees in n o(n) The best lower bound reported is from [1, 2] where it is shown that the star consisting of n ....

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Roberts, Alan, Antonis Symvonis, and Louxin Zhang, "Routing on Trees via Matchings." In Lecture Notes of Computer Science, Vol. 955: 4th Workshop on Algorithms and Data Structures, pages 251 -- 262, 1995.

....have been considered, but, as in our paper, most papers (see e.g. 7, 12, 14, 18, 19, 24, 25, 26, 31] consider the model in which, at each time step, each edge can carry one 2 packet in each direction. Off line construction of routing schedules has been a subject of several papers (see e.g. [1, 3, 16, 27, 29, 30, 33]) Off line constructions do have direct applications in industry [8, 17, 30] but they are also investigated to examine the possibility of constructing on line solutions [15] Hot potato routing schemes, as studied in this paper, have been considered for more than thirty years [5] and the ....

.... as studied in this paper, have been considered for more than thirty years [5] and the running times of hot potato routing schemes have more recently been studied in various networks [4, 6, 10, 13, 29] Trees have always been a subject of special interest in the routing literature (see e.g. [1, 33, 27, 28, 29, 16, 20, 22, 23]) As pointed out by Leighton [17] many networks are simply trees, and, moreover, routing in general graphs may be done using only the edges of a spanning tree of the graph. As mentioned above, our contribution is a near linear construction of direct (hot potato) routing schemes for trees that ....

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A. Roberts, A. Symvonis, and L. Zhang. Routing on trees via matching. In Proceedings of the 4th workshop on algorithms and data structures (WADS'95), pages 251--262, 1995.

....this routing problem for a variety of popular networks including trees, complete (bipartite) graphs, hypercubes, expander graphs and Cayley graphs. One of their interesting results is that any permutation on a tree with n nodes can be routed in at most 3n steps, which was improved to 13 5 n in [13] and then 2n in [5, 7] They also conjecture that the optimal upper bound for trees is 3 2 n. In [13] Roberts, Symvonis and Zhang proved that any permutation can be routed in at most n o(n) steps on an n node d ary complete trees in which the root has degree d and any other internal node has ....

....hypercubes, expander graphs and Cayley graphs. One of their interesting results is that any permutation on a tree with n nodes can be routed in at most 3n steps, which was improved to 13 5 n in [13] and then 2n in [5, 7] They also conjecture that the optimal upper bound for trees is 3 2 n. In [13], Roberts, Symvonis and Zhang proved that any permutation can be routed in at most n o(n) steps on an n node d ary complete trees in which the root has degree d and any other internal node has degree d 1 for some fixed d 0. Furthermore, relation routing under a variant of the matching model ....

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A. Roberts, A. Symvonis and L. Zhang, Routing on trees via matchings, In Proc. of The 4rd Workshop on Algorithms and Data Structures, Kingston, Canada, 1995. Lecture Notes in Computer Sciences, vol. 955, 251-263.

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