On double-link failure recovery in WDM optical networks
Network survivability is a crucial requirement in high-speed optical networks. Typical approaches of providing survivability have considered the failure of a single component such as a link or a node. We consider a failure model in which any two links in the network may fail in an arbitrary order. Three loopback methods of recovering from double-link failures are presented. The first two methods require the identification of the failed links, while the third one does not. However, precomputing the backup paths for the third method is more difficult than for the first two. A heuristic algorithm that pre-computes backup paths for links is presented. Numerical results comparing the performance of our algorithm with other approaches suggests that it is possible to achieve 100% recovery from double-link failures with a modest increase in backup capacity.

title: Hardness on IP-subnet Aware Routing in WDM Network
abstract: In this paper, we study the hardness of the IP-subnet aware routing problem in WDM network. IP-subnet aware routing attempts to reduce routing overhead by grouping a set of addresses under a single subnet. However, routing in WDM network with subnets imposes neighboring IP interfaces along the path to be on the same subnet. This subnet constraint forces the routing path to be longer unless routing permits reconfiguration of subnets. The hardness of this routing problem is first studied in . We investigate further the problem of finding paths accounting for subnets and its hardness. Regardless of subnets, we argue that a shortest IP hop path can be constructed in a polynomial time. We provide efficient routing algorithms to justify our argument.

title: Efficient scheduling of transmissions in optical broadcast networks
abstract: All-optical networks (AONs) with a broadcast-star based physical topology offer the possibility of transmission scheduling to resolve channel and receiver conflicts. This paper considers the problem of scheduling packet transmissions in a wavelength-division multiplexed (WDM) optical network with tunable transmitters and fixed-tuned receivers. The scheduling problem is complicated by tuning latency, a limited number of channels, and arbitrary traffic demands. We first analyze scheduling all-to-all packet transmissions and obtain a new lower bound for the schedule length. The lower bound is achieved by an algorithm proposed by Pieris and Sasaki (1994). We then extend the analysis to the case of arbitrary traffic demands and obtain lower bounds for the schedule length. Two constructions for scheduling algorithms are provided through list scheduling and multigraphs. The upper bounds so obtained not only provide performance guarantees with arbitrary demands, but also nearly meet the lower bound in simulations.

title: Dual power management for network connectivity in wireless sensor networks
abstract: As the energy consumption in wireless sensor nodes is dominated by the radio transmission circuitry, the network configuration must be designed to minimize the power consumption by transmission radios. Sensor nodes are generally equipped with short-range radios that require low power consumption. But the current technology allows each node to adjust its transmission power. We consider the dual power radios in which the radio of each node can be assigned high-or low-power during the network initializing stage. Our primary goal in such an assignment is to minimize the overall power consumption by radios to maximize the network lifetime while maintaining the full network connectivity, the most fundamental network functionality. Using a graph-theoretic approach, we formulate the problem as a "minimum subgraph" problem, show its NP-completeness, establish upper and lower bounds on the optimum solution, and present a near-optimal heuristic algorithm and simulation results.

title: Loopback recovery from neighboring double-link failures in WDM mesh networks
abstract: Traditional survivable network design assumes that at any time at most a single link or node fails. In optical networks, a single point of failure may lead to the failure of multiple links. In this paper, we consider the design of an optical network that can survive the failures of any two neighboring links. We present a loopback recovery method that requires the computation of backup paths for each link. An optimal algorithm for computing the backup paths is presented. Numerical results comparing the performance of our algorithm with other loopback approaches indicate that a slight increase in capacity can achieve 100% protection under this failure model.

title: Efficient route establishment and maintenance in wireless sensor networks with mobile base stations
abstract: The integration of ground wireless adhoc networks and airborne UAVs is a promising solution for realtime data collection in wireless sensor networks. Such networks play a vital role in many mission critical tasks such as forest fire-fighting and battlefield support. An important problem is to establish/maintain efficient routing structures in the ground sensor network for packet relaying. Our problem is unique in that the base stations are non-static, which necessitates frequent update of the routing structure. The performance of flooding based methods are evaluated. Particularly, in order to deal with non-uniform node density, we propose to introduce an artificial delay factor to control the flooding pattern. We mathematically prove that the delay should be proportional to local node density. Our simulation results show that the proposed method achieves good load balance among multiple base stations.

title: Link-disjoint embedding of complete binary trees in meshes

title: Medial axis transform and offset curves by Minkowski Pythagorean hodograph curves
abstract: We present a new approach to medial axis transform and offset curve computation. Our algorithm is based on the domain decomposition scheme which reduces a complicated domain into a union of simple subdomains each of which is very easy to handle. This domain decomposition approach gives rise to the decomposition of the corresponding medial axis transform which is regarded as a geometric graph in the three dimensional Minkowski space R 2,1 . Each simple piece of the domain, called the fundamental domain, corresponds to a space-like curve in R 2,1 . Then using the new spline, called the Minkowski Pythagorean hodograph curve which was recently introduced, we approximate within the desired degree of accuracy the curve part of the medial axis transform with a G 1 cubic spline of Minkowski Pythagorean hodograph. This curve has the property of enabling us to write all offset curves as rational curves. Further, this Minkowski Pythagorean hodograph curve representation together with the domain decomposition lemma makes the trimming process essentially trivial. We give a simple procedure to obtain the trimmed offset curves in terms of the radius function of the MPH curve representing the medial axis transform.

title: Analyzing the Performance of Mesh and Fat-Tree Topologies for Network on Chip Design
abstract: The demand of integration of many heterogeneous semiconductor intellectual property (IP) blocks has been introducing a new chip design paradigm so called on chip network. This paradigm promisingly offers a packet switched network among IPs to reduce the main problems in the very deep sub micron technologies that arise from non-scalable global wire delay, failure to achieve global synchronization, errors due to the signal integrity, non-scalable bus based functional interconnection, etc. This paper introduces interconnected or switched network topologies and also analyze their performances in terms of communication protocol related to the issues such as routing strategy, buffer size, routing algorithm , etc. The above mentioned evaluations are done by utilizing the tool that has been widely used in the research domain of computer network design, so called NS-2.

title: Establishing Pair-Wise Keys in Heterogeneous Sensor Networks
abstract: Many applications that make use of sensor networks require secure communication. Because asymmetric-key solutions are difficult to implement in such a resource-constrained environment, symmetric-key methods coupled with a priori key distribution schemes have been proposed to achieve the goals of data secrecy and integrity. These approaches typically assume that all sensors are similar in terms of capabilities, and hence deploy the same number of keys in all sensors in a network to provide the aforementioned protections. In this paper we demonstrate that a probabilistic unbalanced distribution of keys throughout the network that leverages the existence of a small percentage of more capable sensor nodes can not only provide an equal level of security but also reduce the consequences of node compromise. We demonstrate the effectiveness of this approach on small networks using a variety of trust models and then demonstrate the application of this method to very large systems. The approach and analysis presented in this paper can be applied to all protocols that use probabilistic keys including those that employ broadcast mechanisms, hash functions or polynomials for the generation of keys.

title: Almost rotation-minimizing rational parametrization of canal surfaces
abstract: Almost rotation minimizing parametrization of the canal surface is given. The basic building block of our approach is the curve approximation scheme that enables us to construct a curve, called the parameter curve, on the canal surface that produces, when projected and rescaled, an almost parallel normal vector field on the spine curve. Its construction relies on our earlier methods and results on relating the geometry of the canal surface to the Lorentzian geometry of the Minkowski geometry via the Clifford algebra formalism. We then iteratively construct patches out of the parameter curves via suitable interpolation procedure. Furthermore, its rotational deviation, i.e., the angle deviation from the parallel (no rotation) frame along the spine curve, can be controlled with the use of the rotation deviation estimate of the parameter curves. Our numerical experiment shows that the rotation deviation is minuscule. When compared with other earlier results including our earlier one, our result fares extremely favorably. To facilitate the implement, a practitioners' summary is given in the appendix.