7001903
Distributed object location in a dynamic network
Modern networking applications replicate data and services widely, leading to a need for location-independent routing -- the ability to route queries directly to objects using names independent of the objects' physical locations. Two important properties of a routing infrastructure are routing locality and rapid adaptation to arriving and departing nodes. We show how these two properties can be efficiently achieved for certain network topologies. To do this, we present a new distributed algorithm that can solve the nearest-neighbor problem for these networks. We describe our solution in the context of Tapestry, an overlay network infrastructure that employs techniques proposed by Plaxton, Rajaraman, and Richa [14].
125992802
A tight bound on approximating arbitrary metrics by tree metrics
In this paper, we show that any n point metric space can be embedded into a distribution over dominating tree metrics such that the expected stretch of any edge is O(log n). This improves upon the result of Bartal who gave a bound of O(log n log log n). Moreover, our result is existentially tight; there exist metric spaces where any tree embedding must have distortion Ω(log n)-distortion. This problem lies at the heart of numerous approximation and online algorithms including ones for group Steiner tree, metric labeling, buy-at-bulk network design and metrical task system. Our result improves the performance guarantees for all of these problems.
96030
Beyond the flow decomposition barrier
We introduce a new approach to the maximum flow problem. This approach is based on assigning arc lengths based on the residual flow value and the residual arc capacities. Our approach leads to an <italic>O</italic>(min(<italic>n</italic><supscrpt>2/3</supscrpt>, <italic>m</italic><supscrpt>1/2</supscrpt>)<italic>m</italic> log(<italic>n</italic><supscrpt>2</supscrpt>/<italic>m</italic>) log <italic>U</italic>) time bound for a network with <italic>n</italic> vertices, <italic>m</italic> arcs, and integral arc capacities in the range [1, …, <italic>U</italic>]. This is a fundamental improvement over the previous time bounds. We also improve bounds for the Gomory-Hu tree problem, the parametric flow problem, and the approximate <italic>s-t</italic>  cut problem.
11142529
Segmentation of hybrid motions via hybrid quadratic surface analysis
In this paper, we investigate the mathematical problem underlying segmentation of hybrid motions: given a series of tracked feature correspondences between two (perspective) images, we seek to segment and estimate multiple motions, possibly of different types (e.g., affine, epipolar, and homography). In order to accomplish this task, we cast the problem into a more general mathematical framework of segmenting data samples drawn from a mixture of linear subspaces and quadratic surfaces. The result is a novel algorithm called hybrid quadratic surface analysis (HQSA). HQSA uses both the derivatives and Hessians of fitting polynomials for the data to separate linear data samples from quadratic data samples. These derivatives and Hessians also lead to important necessary conditions, based on the so-called mutual contraction subspace, to separate data samples on different quadratic surfaces. The algebraic solution we derive is non-iterative and numerically stable. It tolerates moderate noise and can be used in conjunction with outlier removal techniques. We show how to solve the hybrid motion segmentation problem using HQSA, and demonstrate its performance on simulated data with noise and on real perspective images.
7179412
Considering Priority in Overlay Multicast Protocols Under Heterogeneous Environments
Hosts participating in overlay multicast applications have a wide range of heterogeneity in bandwidth and participation characteristics. In this paper, we highlight and show the need to systematically consider prioritization as a key criterion in the design of protocols for overlay multicast. We identify trade-offs in the design of prioritization heuristics in two important contexts. The first part of the paper considers prioritization strategies in the context of heterogeneity in node outgoing bandwidth and node stay time durations, and a lack of correlation between the two dimensions. The second part of the paper considers bandwidth allocation and prioritization policies with multi-tree data delivery in environments with heterogeneity in outgoing bandwidth and a certain degree of altruistic behavior. We conduct a systematic study of the trade-offs using both real trace data, and sensitivity studies using synthetic workloads. To the best of our knowledge, this is the first work to identify and study these trade-offs, and to demonstrate the potential benefits of the resulting prioritization heuristics.
205492674
Spectra and energies of iterated line graphs of regular graphs
If G is a graph and L(G)=L1(G) its line graph, then Lk(G), k=2,3,…, defined recursively via Lk(G)=L(Lk−1(G)), are the iterated line graphs of G. If G is a regular graph of degree r, r≥3, then all negative eigenvalues of its iterated line graphs are equal to minus 2. The energy E(G) of a graph G is the sum of absolute values of the eigenvalues of G. If G is a regular graph of order n and of degree r≥3, then for each k≥2, E(Lk(G)) depends solely on n and r. In particular, E(L2(G))=2nr(r−2). This result enables a systematic construction of pairs of non-cospectral connected graphs of the same order, having equal energies.
36356018
Solution of the Hamiltonian problem for self-complementary graphs
Abstract A graph G is said to be highly constricted if there exists a nonempty subset S of vertices such that (i) G − S has more than | S | components, (ii) S induces the complete graph, and (iii) for every u ∈ S and v ∉ S , we have d G ( u ) > d G ( v ), where d G ( u ) denotes the degree of u in G . In this paper it is shown that a non-hamiltonian self-complementary graph G of order p is highly constricted, unless p = 4 N and G is a particular graph G ∗ (4N) . It is also proved that if G is a self-complementary graph of order p (≥8) and π its degree sequence, then G is pancyclic if π has a realization with a hamiltonian cycle, and G has a 2-factor if π has a realization with a 2-factor, unless p = 4 N and G = G ∗ (4N) .
17940922
Symmetry-based 3-D reconstruction from perspective images
Symmetry is an important geometric cue for 3-D reconstruction from perspective images. In this paper, we introduce a unified theoretical framework for extracting poses and structures of 2-D symmetric patterns in space from calibrated images. The framework uniformly encompasses all three fundamental types of symmetry, i.e., reflective, rotational, and translational, based on a systematic study of the homography groups in image induced by the symmetry groups in space. We claim that if a planar object admits rich enough symmetry, no 3-D geometric information is lost through perspective imaging. Based on two fundamental principles that utilize common spatial relations among symmetric objects, we have developed a prototype system which can automatically extract and segment multiple 2-D symmetric patterns present in a single perspective image. The result of such a segmentation is a hierarchy of new geometric primitives, called symmetry cells and complexes, whose 3-D structures and poses are fully recovered. Finally, we propose a new symmetry-based matching technique, which can effectively establish correspondences among the extracted symmetry cells across multiple images. We demonstrate the application of the proposed algorithms on image segmentation, matching, and 3-D reconstruction with extensive experimental results. The algorithms and systems are more accurate and easier to implement than existing point-or line-based methods.