16222163
Learning a Hidden Hypergraph
We consider the problem of learning a hypergraph using edge-detecting queries. In this model, the learner may query whether a set of vertices induces an edge of the hidden hypergraph or not. We show that an r-uniform hypergraph with m edges and n vertices is learnable with O(2 4r m.poly(r,logn)) queries with high probability. The queries can be made in O(min(2 r r 2 log 2 n, r 3 log 3 n)) rounds. We also give an algorithm that learns a non-uniform hypergraph whose minimum edge size is r 1 and maximum edge size is r 2 using O(f 1 (r 1 ,r 2 ).m (r 2 -r 1 +2)/2 . poly(log n)) queries with high probability, and give a lower bound of Ω(f 2 (r 1 ,r 2 ).m (r 2 -r 1 +2)/2 for this class of hypergraphs, where fi and f 2 are functions depending only on r 1 and r 2 . The queries can also be made in O(min(2 r 2r 2 2 log 2 n, r 3 2 log 3 n)) rounds.
8876890
Overlay mesh construction using interleaved spanning trees
In this paper we evaluate a method of using interleaved spanning trees to compose a resilient, high performance overlay mesh. Though spanning trees of arbitrary type could be used to construct an overlay mesh, we focus on a distributed algorithm that computes k minimum spanning trees on an arbitrary graph. The principal motivation behind this strategy is to provide applications with a k-redundant, high quality mesh suitable for demanding applications like A/V broadcast, video conferencing, data collection, multi-path routing, and file mirroring/transfer. We elaborate details of k-MST, pointing out advantages and potential problem points of the protocol, and then analyze its performance using a variety of metrics with simulation as well as a functional PlanetLab implementation.
12471299
Kernels for small molecules and the prediction of mutagenicity, toxicity and anti-cancer activity
MOTIVATION
Small molecules play a fundamental role in organic chemistry and biology. They can be used to probe biological systems and to discover new drugs and other useful compounds. As increasing numbers of large datasets of small molecules become available, it is necessary to develop computational methods that can deal with molecules of variable size and structure and predict their physical, chemical and biological properties.


RESULTS
Here we develop several new classes of kernels for small molecules using their 1D, 2D and 3D representations. In 1D, we consider string kernels based on SMILES strings. In 2D, we introduce several similarity kernels based on conventional or generalized fingerprints. Generalized fingerprints are derived by counting in different ways subpaths contained in the graph of bonds, using depth-first searches. In 3D, we consider similarity measures between histograms of pairwise distances between atom classes. These kernels can be computed efficiently and are applied to problems of classification and prediction of mutagenicity, toxicity and anti-cancer activity on three publicly available datasets. The results derived using cross-validation methods are state-of-the-art. Tradeoffs between various kernels are briefly discussed.


AVAILABILITY
Datasets available from http://www.igb.uci.edu/servers/servers.html
2426986
Quantifying Privacy Leakage through Answering Database Queries
We assume a database consists of records of individuals with private or sensitive fields. Queries on the distribution of a sensitive field within a selected population in the database can be submitted to the data center. The answers to the queries leak private information of individuals though no identification information is provided. Inspired by decision theory, we present a quantitative model for the privacy protection problem in such a database query or linkage environment in this paper. In the model, the value of information is estimated from the viewpoint of the querier.To estimate the value, we define the information state of the data user by a class of probability distributions on the set of possible confidential values. We further define the usefulness of information based on how easy the data user can locate individuals that fit the description given in the queries. These states and the usefulness of information can be modified and refined by the user's knowledge acquisition actions. The value of information is then defined as the expected gain of the privacy receiver and the privacy is protected by imposing costs on the answers of the queries for balancing the gain.
932171
On strong Menger-connectivity of star graphs
Motivated by parallel routing in networks with faults, we study the following graph theoretical problem. Let G be a graph of minimum vertex degree d. We say that G is strongly Menger-connected if for any copy Gf of G with at most d - 2 nodes removed, every pair of nodes u and v in Gf are connected by min{degf(u), degf(v)} node-disjoint paths in Gf, where degf(u) and degf(v) are the degrees of the nodes u and v in Gf, respectively. We show that the star graphs, which are a recently proposed attractive alternative to the widely used hypercubes as network models, are strongly Menger-connected. An algorithm of optimal running time is developed that constructs the maximum number of node-disjoint paths of nearly optimal length in star graphs with faults.
117657252
Labeled Search Trees and Amortized Analysis: Improved Upper Bounds for NP-Hard Problems
A sequence of exact algorithms to solve the Vertex Cover and Maximum Independent Set problems have been proposed recently in the literature. All these algorithms appeal to a very conservative analysis that considers the size of the search tree, under a worst-case scenario, to derive an upper bound on the running time of the algorithm. In this paper we propose a different approach to analyze the size of the search tree. We use amortized analysis to show how simple algorithms, if analyzed properly, may perform much better than the upper bounds on their running time derived by considering only a worst-case scenario. This approach allows us to present a simple algorithm of running time O(1.194 k + n) for the parameterized Vertex Cover problem on degree-3 graphs, and a simple algorithm of running time O(1.1254 n ) for the Maximum Independent Set problem on degree-3 graphs. Both algorithms improve the previous best algorithms for the problems.
13557005
Vertex Cover: Further Observations and Further Improvements
Recently, there has been increasing interest and progress in lowering the worst-case time complexity for well-known NP-hard problems, particularly for the Vertex Cover problem. In this paper, new properties for the Vertex Cover problem are indicated, and several simple and new techniques are introduced, which lead to an improved algorithm of time O(kn+1.2852k) for the problem. Our algorithm also induces improvement on previous algorithms for the Independent Set problem on graphs of small degree.