Algorithms And Data Structures

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Additional info for Algorithms for Delta Compression and Remote File Synchronization

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We refer to this problem as the Generalized Priority Steiner problem (or GPS). In this work we address priority Steiner tree problems from the point of view of online algorithms, in that the set K of terminals in PST (or pairs of terminals in GPS) is not known to the algorithm in advance, but instead is revealed as a sequence of requests. This models the situation in which subscribers to a multicast group are not predetermined, but rather issue dynamic requests to join a group. Thus it is not surprising that many variants of Steiner tree problems have been studied extensively in the on-line setting (see also Section 1).

Straight-Line Rectangular Drawings of Clustered Graphs 27 Such a stronger result is proved by means of an inductive algorithm reminiscent of Fary’s drawing algorithm for planar graphs [9]. Namely, the algorithm consists of three inductive cases. Each case considers a clustered graph C and performs an operation (removal of a cluster, split of the graph in correspondence of a separating 3-cycle, contraction of an edge) turning C into a smaller clustered graph C , for which a straight-line rectangular drawing can be inductively constructed.

Such an algorithm is presented in Sect. 3. Omitted and sketched proofs can be found in the full version of the paper [1]. 2 Preliminaries Let C(G, T ) be a clustered graph. An edge (u, v) of G is incident to a cluster μ of T if u belongs to μ and v does not. Let σ(u1 , u2 , . . , uk ) be the smallest cluster of T containing vertices u1 , u2 , . . , the node of T containing all of u1 , u2 , . . , uk and such that none of its children in T , if any, contains all of u1 , u2 , . . , uk . A cluster is minimal if it contains no other cluster.

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Algorithms for Delta Compression and Remote File Synchronization by Suel Memon


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