Motivated by privacy preservation for outsourced data, data-oblivious external memory is a computational framework where a client performs computations on data stored at a semi-trusted server in a way that does not reveal her data to the server. This approach facilitates collaboration and reliability over traditional frameworks, and it provides privacy protection, even though the server has full access to the data and he can monitor how it is accessed by the client. The challenge is that even if data is encrypted, the server can learn information based on the client data access pattern; hence, access patterns must also be obfuscated. We investigate privacy-preserving algorithms for outsourced external memory that are based on the use of data-oblivious algorithms, that is, algorithms where each possible sequence of data accesses is independent of the data values. We give new efficient data-oblivious algorithms in the outsourced external memory model for a number of fundamental graph problems. Our results include new data-oblivious external-memory methods for constructing minimum spanning trees, performing various traversals on rooted trees, answering least common ancestor queries on trees, computing biconnected components, and forming open ear decompositions. None of our algorithms make use of constant-time random oracles. arXiv:1409.0597v1 [cs.DS] 2 Sep 2014interface that allows her to make read and write requests of Bob using messages of size B as atomic actions. We also assume Alice has a small amount of secure, private working memory, of size M = Ω(log N ).The server, Bob, is "honest-but-curious," which means that he will correctly perform every task requested, but he will also try to learn as much as possible about Alice's data. This, of course, introduces privacy constraints for the DO-OEM model not found in the traditional I/O model (such as in [6]). In particular, we can rely on Bob to faithfully execute read and write requests, but he would like to learn as much as possible about Alice's data. Thus, Alice must encrypt her data and then decrypt it and re-encrypt it with each read and write request, using a semantically-secure encryption scheme. Alice can safely perform any computation in her private memory, but her sequence of data accesses on the server must also not leak information about her data. That is, it must be data oblivious. The access sequence may depend on the function being computed, but it should be independent of the input data values.Formally, we suppose Alice wants to perform an algorithm, A, which computes some function, f , on her data stored with Bob. In the context of graph algorithms, the input to f is a graph, usually formatted as an array of edges, with V and E being the number of the graph's vertices and edges, respectively. The output of f may either be a property of the graph, such as whether or not the graph is biconnected, or another graph, such as a spanning tree, which will also be stored with Bob. Alice performs the algorithm A by issuing read and write requests to Bob.We s...
4We study planar point location in a collection of disjoint fat regions, and investigate the complexity of local 5 updates: replacing any region by a different region that is "similar" to the original region. (i.e., the size 6 differs by at most a constant factor, and distance between the two regions is a constant times that size).
We show that a transitively reduced digraph has a confluent upward drawing if and only if its reachability relation has order dimension at most two. In this case, we construct a confluent upward drawing with O(n 2 ) features, in an O(n) × O(n) grid in O(n 2 ) time. For the digraphs representing series-parallel partial orders we show how to construct a drawing with O(n) features in an O(n) × O(n) grid in O(n) time from a series-parallel decomposition of the partial order. Our drawings are optimal in the number of confluent junctions they use.
Abstract. We investigate exact crossing minimization for graphs that differ from trees by a small number of additional edges, for several variants of the crossing minimization problem. In particular, we provide fixed parameter tractable algorithms for the 1-page book crossing number, the 2-page book crossing number, and the minimum number of crossed edges in 1-page and 2-page book drawings.
We show that several problems of compacting orthogonal graph drawings to use the minimum number of rows, area, length of longest edge or total edge length cannot be approximated better than within a polynomial factor of optimal in polynomial time unless P = NP. We also provide a fixed-parameter-tractable algorithm for testing whether a drawing can be compacted to a small number of rows.
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