P.M. Camerini, L. Fratta, and F. Ma#oli. A note on finding optimum branchings. Networks, 9:309--312, 1979.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....file per compressed file, this problem is equivalent to finding an optimum branching in a corresponding directed graph where each edge has a weight equal to size of the delta of with respect to reference file . This problem can be solved in time quadratic in the number of documents [12, 42], but the approach suffers from two drawbacks: First, the solution may contain very long chains of documents that have to be accessed in order to uncompress a particular file. Second, for large collections the quadratic time becomes unacceptable, particularly the cost of computing the appropriate ....

P. Camerini, L. Fratta, and F. Maffioli. A note on finding optimum branchings. Networks, 9:309--312, 1979.

....LZ distance that is closely related to the performance of Lempel Ziv type compressing schemes. We also refer to [6] and the references therein for work on protocols for estimating file similarities over a communication link. Fast algorithms for the optimum branching problem are described in [4, 22]. While we are not aware of previous work that uses optimum branchings to compress collections of files, there are two previous applications that are quite similar. In particular, Tate [23] uses optimum branchings to find an optimal scheme for compressing multispectral images, while Adler and ....

....i.e. file is compressed by itself, files are compressed by computing a delta with respect to file , and file is compressed by computing a delta with respect to file . 2. 2 Experimental Results We implemented delta compression based on the optimal branching algorithm described in [4, 22], which for dense graphs takes time proportional to the number of edges. Table 1 shows compression results and times on several collections of web pages that we collected by crawling a limited number of pages from each site using a breadth first crawler. The results indicate that the optimum ....

P. Camerini, L. Fratta, and F. Maffioli. A note on finding optimum branchings. Networks, 9:309--312, 1979.

....LZ distance that is closely related to the performance of Lempel Ziv type compressing schemes. We also refer to [6] and the references therein for work on protocols for estimating file similarities over a communication link. Fast algorithms for the optimum branching problem are described in [4, 22]. While we are not aware of previous work that uses optimum branchings to compress collections of files, there are two previous applications that are quite similar. In particular, Tate [23] uses optimum branchings to find an optimal scheme for compressing multispectral images, while Adler and ....

...., i.e. file is compressed by itself, files are compressed by computing a delta with respect to file , and file is compressed by computing a delta with respect to file . 2. 2 Experimental Results We implemented delta compression based on the optimal branching algorithm described in [4, 22], which for dense graphs takes time proportional to the number of edges. Table 1 shows compression results and times on several collections of web pages that we collected by crawling a limited number of pages from each site using a breadth first crawler. The results indicate that the optimum ....

P. Camerini, L. Fratta, and F. Maffioli. A note on finding optimum branchings. Networks, 9:309--312, 1979.

....most nonzero entries in (MM ) the total time required to compute the graph G S is O (n ) Computing a minimum directed spanning tree with root r in a directed graph is generally referred to in the literature as a branching with root r. For information on branchings, see for example [6, 8, 10, 16]. Minimum spanning trees in directed graphs with x nodes and y edges can be found deterministically in time O(x log x y) 8] A simpler algorithm that runs in time O(y log x) is suitable for the case of sparse graphs [16, 6] which will generally be the case in our context. Since the total ....

....with root r. For information on branchings, see for example [6, 8, 10, 16] Minimum spanning trees in directed graphs with x nodes and y edges can be found deterministically in time O(x log x y) 8] A simpler algorithm that runs in time O(y log x) is suitable for the case of sparse graphs [16, 6], which will generally be the case in our context. Since the total number of edges in G S is at most n, the total time required to compute the minimum directed spanning tree in G S is O (n log n ) All that remains is to perform the compression using the computed directed tree to specify ....

P. M. Camerini, L. Fratta, and F. Maffioli. A note on finding optimum branchings. Networks, 9:309-312, 1979.

....in (MM T ) the total time required to compute the graph G S is O (n P n i=1 t GW (i) 2 ) Computing a minimum directed spanning tree with root r in a directed graph is generally referred to in the literature as a branching with root r. 1 For information on branchings, see for example [7, 9, 11, 19]. Minimum spanning trees in directed graphs with x nodes and y edges can be found deterministically in time O(x log x y) 9] A simpler algorithm that runs in time O(y log x) is suitable for the case of sparse graphs [19, 7] which will generally be the case in our context. Since the total number ....

....with root r. 1 For information on branchings, see for example [7, 9, 11, 19] Minimum spanning trees in directed graphs with x nodes and y edges can be found deterministically in time O(x log x y) 9] A simpler algorithm that runs in time O(y log x) is suitable for the case of sparse graphs [19, 7], which will generally be the case in our context. Since the total number of edges in G S is at most P n i=1 t GW (i) 2 n, the total time required to compute the minimum directed spanning tree in G S is O (n log n P n i=1 t GW (i) 2 ) All that remains is to perform the ....

P. M. Camerini, L. Fratta, and F. Maffioli. A note on finding optimum branchings. Networks, 9:309-312, 1979.

....) Then, finding the optimal joining of all k ZSTs is equivalent to finding the optimal branching in G, i.e. the minimum cost subgraph of G containing paths from a single node to all others. The optimal branching problem was first addressed by Tarjan and by Camerini et al. in the late 1970s [20] [2]; an optimal solution can be found in time O(k 2 ) using Edmonds algorithm as implemented in [11] 3.3 Heuristic H2: Optimal Slice Merging Even the optimal joining of one tree s root into another tree can waste a great deal of wiring. We say that the merging of tree A into tree B entails ....

P. M. Camerini, L. Fratta and F. Maffioli, "A note on finding optimum branchings ", Networks 9 (1979), pp. 309-312.

....of any band ordering, or the optimal compression order of the bands of the multispectral image. It is known that a maximum weight directed spanning forest (also known as an optimal branching ) can be found in O(jV j log jEj jEj) time on sparse graphs and O(jV j 2 ) time on dense graphs [7, 8], so it follows that an optimal compression order can be found in O(n 2 ) time. The graph G that is derived from the sample A and B matrices of Figure 1 is shown in Figure 2, where dashed and solid lines both represent graph edges, and the solid lines are the edges that are part of the maximum ....

P. M. Camerini, L. Fratta, and F. Maffioli, "A note on finding optimum branchings," Networks, vol. 9, pp. 309--312, 1979.

....of any band ordering, or the optimal compression order of the bands of the multispectral image. It is known that a maximum weight directed spanning forest (also known as an optimal branching ) can be found in O(jV j log jEj jEj) time on sparse graphs and O(jV j 2 ) time on dense graphs [13, 2], so it follows that an optimal compression order can be found in O(n 2 ) time. The graph G that is derived from the sample A and B matrices of Figure 1 is shown in Figure 2, where dashed and solid lines both represent graph edges, and the solid lines are the edges that are part of the maximum ....

P. M. Camerini, L. Fratta, and F. Maffioli. "A Note on Finding Optimum Branchings," Networks, Vol. 9, pp. 309--312, 1979.

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P.M. Camerini, L. Fratta, and F. Ma#oli. A note on finding optimum branchings. Networks, 9:309--312, 1979.

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Camerini, P., L. Fratta, and F. Maffioli. A note on finding optimum branchings. Networks 9, 309--312, 1979.

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