Improved Approximation Algorithms for Computing k Disjoint Paths Subject to Two Constraints

For a given graph $G$ with positive integral cost and delay on edges, distinct vertices $s$ and $t$, cost bound $C\in Z^{+}$ and delay bound $D\in Z^{+}$, the $k$ bi-constraint path ($k$BCP) problem is to compute $k$ disjoint $st$-paths subject to $C$ and $D$. This problem is known NP-hard, even when $k=1$ \cite{garey1979computers}. This paper first gives a simple approximation algorithm with factor-$(2,2)$, i.e. the algorithm computes a solution with delay and cost bounded by $2*D$ and $2*C$ respectively. Later, a novel improved approximation algorithm with ratio $(1+\beta,\,\max\{2,\,1+\ln\frac{1}{\beta}\})$ is developed by constructing interesting auxiliary graphs and employing the cycle cancellation method. As a consequence, we can obtain a factor-$(1.369,\,2)$ approximation algorithm by setting $1+\ln\frac{1}{\beta}=2$ and a factor-$(1.567,\,1.567)$ algorithm by setting $1+\beta=1+\ln\frac{1}{\beta}$. Besides, by setting $\beta=0$, an approximation algorithm with ratio $(1,\, O(\ln n))$, i.e. an algorithm with only a single factor ratio $O(\ln n)$ on cost, can be immediately obtained. To the best of our knowledge, this is the first non-trivial approximation algorithm for the $k$BCP problem that strictly obeys the delay constraint.Comment: 12 page

What cost reslience?

Air traffic management research lacks a framework for modelling the cost of resilience during disturbance. There is no universally accepted metric for cost resilience. The design of such a framework is presented and the modelling to date is reported. The framework allows performance assessment as a function of differential stakeholder uptake of strategic mechanisms designed to mitigate disturbance. Advanced metrics, cost- and non-cost-based, disaggregated by stakeholder subtypes, will be deployed. A new cost resilience metric is proposed

Implications of Motion Planning: Optimality and k-survivability

We study motion planning problems, finding trajectories that connect two configurations of a system, from two different perspectives: optimality and survivability. For the problem of finding optimal trajectories, we provide a model in which the existence of optimal trajectories is guaranteed, and design an algorithm to find approximately optimal trajectories for a kinematic planar robot within this model. We also design an algorithm to build data structures to represent the configuration space, supporting optimal trajectory queries for any given pair of configurations in an obstructed environment. We are also interested in planning paths for expendable robots moving in a threat environment. Since robots are expendable, our goal is to ensure a certain number of robots reaching the goal. We consider a new motion planning problem, maximum k-survivability: given two points in a stochastic threat environment, find n paths connecting two given points while maximizing the probability that at least k paths reach the goal. Intuitively, a good solution should be diverse to avoid several paths being blocked simultaneously, and paths should be short so that robots can quickly pass through dangerous areas. Finding sets of paths with maximum k-survivability is NP-hard. We design two algorithms: an algorithm that is guaranteed to find an optimal list of paths, and a set of heuristic methods that finds paths with high k-survivability

A cross-layer quality-oriented energy-efficient scheme for multimedia delivery in wireless local area networks

Wireless communication technologies, although emerged only a few decades ago, have grown fast in both popularity and technical maturity. As a result, mobile devices such as Personal Digital Assistants (PDA) or smart phones equipped with embedded wireless cards have seen remarkable growth in popularity and are quickly becoming one of the most widely used communication tools. This is mainly determined by the flexibility, convenience and relatively low costs associated with these devices and wireless communications. Multimedia applications have become by far one of the most popular applications among mobile users. However this type of application has very high bandwidth requirements, seriously restricting the usage of portable devices. Moreover, the wireless technology involves increased energy consumption and consequently puts huge pressure on the limited battery capacity which presents many design challenges in the context of battery powered devices. As a consequence, power management has raised awareness in both research and industrial communities and huge efforts have been invested into energy conservation techniques and strategies deployed within different components of the mobile devices. Our research presented in this thesis focuses on energy efficient data transmission in wireless local networks, and mainly contributes in the following aspects: 1. Static STELA, which is a Medium Access Control (MAC) layer solution that adapts the sleep/wakeup state schedule of the radio transceiver according to the bursty nature of data traffic and real time observation of data packets in terms of arrival time. The algorithm involves three phases– slow start phase, exponential increase phase, and linear increase phase. The initiation and termination of each phase is self-adapted to real time traffic and user configuration. It is designed to provide either maximum energy efficiency or best Quality of Service (QoS) according to user preference. 2. Dynamic STELA, which is a MAC layer solution deployed on the mobile devices and provides balanced performance between energy efficiency and QoS. Dynamic STELA consists of the three phase algorithm used in static STELA, and additionally employs a traffic modeling algorithm to analyze historical traffic data and estimate the arrival time of the next burst. Dynamic STELA achieves energy saving through intelligent and adaptive increase of Wireless Network Interface Card (WNIC) sleeping interval in the second and the third phase and at the same time guarantees delivery performance through optimal WNIC waking timing before the estimated arrival of new data burst. 3. Q-PASTE, which is a quality-oriented cross-layer solution with two components employed at different network layers, designed for multimedia content delivery. First component, the Packet/ApplicaTion manager (PAT) is deployed at the application layer of both service gateway and client host. The gateway level PAT utilizes fast start, as a widely supported technique for multimedia content delivery, to achieve high QoS and shapes traffic into bursts to reduce the wireless transceiver’s duty cycle. Additionally, gateway-side PAT informs client host the starting and ending time of fast start to assist parameter tuning. The client-side PAT monitors each active session and informs the MAC layer about their traffic-related behavior. The second component, dynamic STELA, deployed at MAC layer, adaptively adjusts the sleep/wake-up behavior of mobile device wireless interfaces in order to reduce energy consumption while also maintaining high Quality of Service (QoS) levels. 4. A comprehensive survey on energy efficient standards and some of the most important state-of-the-art energy saving technologies is also provided as part of the work