We study the problem of constructing universal Steiner trees for undirected graphs. Given a graph G and a root node r, we seek a single spanning tree T of minimum stretch, where the stretch of T is defined to be the maximum ratio, over all terminal sets X, of the cost of the minimal sub-tree TXof T that connects X to r to the cost of an optimal Steiner tree connecting X to r in G. Universal Steiner trees (USTs) are important for data aggregation problems where computing the Steiner tree from scratch for every input instance of terminals is costly, as for example in low energy sensor network applications. graphs with 2O(√log n)-stretch. We also give a polynomial time We provide a polynomial time UST construction for general polylog(n)-stretch construction for minor-free graphs. One basic building block of our algorithms is a hierarchy of graph partitions, each of which guarantees small strong diameter for each cluster and bounded neighbourhood intersections for each node. We show close connections between the problems of constructing USTs and building such graph partitions. Our construction of partition hierarchies for general graphs is based on an iterative cluster merging procedure, while the one for minor-free graphs is based on a separator theorem for such graphs and the solution to a cluster aggregation problem that may be of independent interest even for general graphs. To our knowledge, this is the first subpolynomial-stretch (o(nε) for any ε >; 0) UST construction for general graphs, and the first polylogarithmic-stretch UST construction for minor-free graphs.

We consider the problem of implementing transactional memory in large-scale distributed networked systems. We present and analyze Spiral, a novel distributed directory-based protocol for transactional memory. Spiral is designed for the data-flow distributed implementation of software transactional memory which supports three basic operations: publish, allowing a shared object to be inserted in the directory so that other nodes can find it; lookup, providing a read-only copy of the object to the requesting node; move, allowing the requesting node to write the object locally after the node gets it. The protocol runs on a hierarchical directory construction based on sparse covers, where clusters at each level are ordered to avoid race conditions while serving concurrent requests. Given a shared object the protocol maintains a directory path pointing to the object. The basic idea is to use “spiral” paths that grow outward to search for the directory path of the object in a bottom-up fashion. For general networks, this protocol guarantees an O(log2n · log D) approximation for move requests, where n is the number of nodes and D is the diameter of the network. It also guarantees polylog approximation for lookup requests. To the best of our knowledge, this is the first consistency protocol for distributed transactional memory that achieves poly-log approximation in general networks.

We consider the problem of constructing a single spanning tree for the single-sink buy-at-bulk network design problem for doubling-dimension graphs. We compute a spanning tree to route a set of demands along a graph G to or from a designated sink node. The demands could be aggregated at (or symmetrically distributed to) intermediate edges where the fusion cost is specified by a nonnegative concave function f. We describe a novel approach for developing an oblivious spanning tree in the sense that it is independent of the number and location of data sources (or demands) and cost function at the edges. We present a deterministic, polynomial-time algorithm for constructing a spanning tree in low doubling-dimension graphs that guarantees a log3D-approximation over the optimal cost, where D is the diameter of the graph G. With a constant fusion-cost function, our spanning tree gives an O(log3D)-approximation for every Steiner tree that includes the sink. We also provide a Ω(log n) lower bound for any oblivious tree in low doubling-dimension graphs. To our knowledge, this is the first paper to propose a single spanning tree solution to the single-sink buy-at-bulk network design problem (as opposed to multiple overlay trees).

Identification of a low-level point radioactive source amidst background radiation is achieved by a network of radiation sensors using a two-step approach. Based on measurements from three or more sensors, a geometric difference triangulation method or an N -sensor localization method is used to estimate the location and strength of the source. Then a sequential probability ratio test based on current measurements and estimated parameters is employed to finally decide: (1) the presence of a source with the estimated parameters, or (2) the absence of the source, or (3) the insufficiency of measurements to make a decision. This method achieves specified levels of false alarm and missed detection probabilities, while ensuring a close-to-minimal number of measurements for reaching a decision. This method minimizes the ghost-source problem of current estimation methods, and achieves a lower false alarm rate compared with current detection methods. This method is tested and demonstrated using: (1) simulations, and (2) a test-bed that utilizes the scaling properties of point radioactive sources to emulate high intensity ones that cannot be easily and safely handled in laboratory experiments.

Identification of a low-level point radiation source amidst background radiation is achieved by a network of radiation sensors using a two-step approach. Based on measurements from three sensors, the geometric difference triangulation method is used to estimate the location and strength of the source. Then a sequential probability ratio test based on current measurements and estimated parameters is employed to finally decide: (1) the presence of a source with the estimated parameters, or (2) the absence of the source, or (3) the insufficiency of measurements to make a decision. This method achieves specified levels of false alarm and missed detection probabilities, while ensuring a close-to-minimal number of measurements for reaching a decision. This method minimizes the ghost-source problem of current estimation methods, and achieves a lower false alarm rate compared with current detection methods. This method is tested and demonstrated using: (1) simulations, and (2) a test-bed that utilizes the scaling properties of point radiation sources to emulate high intensity ones that cannot be easily and safely handled in laboratory experiments.