Provably good routing tree construction with multi-port terminals

Previous literature on very large scale integration routing and wiring estimation typically assumes a one-to-one correspondence between terminals and ports. In practice, however, each terminal consists of a large collection of electrically equivalent ports, a fact that is not accounted for in layout steps such as wiring estimation. In this paper, we address the general problem of minimum-cost routing tree construction in the presence of multiport terminals, which gives rise to the group Steiner minimal tree problem. Our main result is the first known approximation algorithm for the group Steiner problem with a sublinear performance bound. In particular, for a net with k multiport terminals, previous heuristics have a performance bound of (k-1)/spl middot/OPT, while our construction offers an improved performance bound of 2/spl middot/(2+1n(k/2))/spl middot//spl radic/k/spl middot/OPT. Our Java implementation is available on the Web.

The problem of scheduling and routing tree construction in WiMAX/802.16 based mesh networks is not defined in the standard and has thus been the subject to extensive research. We consider the problem of joint routing and scheduling in WiMAX-based mesh networks, with the objective of determining a minimum schedule period that satisfies a given (uplink/downlink) traffic demand. Minimizing the length of a schedule amounts to maximizing the spectrum spatial reuse by activating concurrently as many links. This group of transmission links active concurrently is referred to as the transmission group and refers to the set of wireless links that can simultaneously transmit without violating the signal-to-interference-plus-noise ratio (SINR) requirement. Our model is referred to as maximum spatial reuse (MSR). We assume centralized scheduling at the base station and attempt to maximize the system throughput through appropriate routing tree selection and achieving efficient spectrum reuse through opportunistic link scheduling. We present an ILP optimization model for the joint problem, which relies on the enumeration of all possible link schedules. Given its complexity, we decompose the problem using a column generation (CG) approach. We present two formulations for modeling MSR, namely the link-based (CGLink) and the path-based (CGPath) formulation. These two formulations differ mainly in the number of routing decision variables. Our experimental results indicate that the path-based formulation needs much less computational (CPU) time than the link-based in order to determine the (same) optimal solution with the same spatial reuse gain.

In deep sub-micron regime, interconnect delays dominate VLSI circuit design. Thus, construction of cost-effective global routing trees is key to such designs. In order to reduce the interconnect delay, traditional Manhattan (M-) routing architectures are currently being replaced by the diagonal X architectures. A recent routing architecture is based on Y interconnects, involving the pervasive use of 0/spl deg/, 60/spl deg/, and 120/spl deg/ oriented global and semi-global wirings. Unlike the X-routing, Y-routing Is observed to support regular routing grid, which as important for simplifying manufacturing processes and routing and design rule checking algorithms. In this paper, we propose a novel Y-routing algorithm which can solve reasonably sized problems in nominal time. The proposed method is capable of finding routing solutions for problem instances which could not be solved in reasonable time by some recently reported methods. Moreover, it can be easily extended for routing with any uniform orientation.

River routing in VLSI

In this paper, we revisit the problem of multicast tree construction in overlay peer-to-peer networks. We present an iterative online multicast tree construction algorithm for multi-session multicasting of elastic content. Our framework allows receivers to request multiple sessions from possibly different servers. Each receiver expresses a quality-of-service requirement using a utility function. We propose an online algorithm which constructs multicast trees to maximize the overall receiver utility functions in an iterative fashion, allowing it to adapt to changes in network topology and cross-traffic.

This paper revisits the problem of multisession multicast tree construction with bandwidth allocation in wireless sensor networks. Previous work has shown that when the goal is to find multicast routing tree, the problem becomes NP-complete. In this work, we present a heuristic Energy-Efficient Multisession Multicast protocol (EEMM) that uses fuzzy logic to evaluate nodes' and network conditions during the multicast tree construction process. Our proposed solution includes an online rate assignment algorithm that aims at maximizing the overall network throughput by accepting as many streams in the network as possible. The proposed solution allows receivers to request multiple sessions from, possibly, different sources with different data rates. We conduct extensive evaluations to study the performance of the proposed protocol compared to other existing approaches, namely shortest path and minimum transmission tree routing. Simulation results show that our protocol effectively improves the network throughput and utilization, while conserving and balancing out per node energy consumption ensure prolonged network lifetime.

Compressive data gathering (CDG) has emerged as a useful method for collecting sensory data in large scale sensor networks; this technique is able to reduce global scale communication cost without introducing intensive computation, and is capable of extending the lifetime of the entire sensor network by balancing the aggregation and forwarding load across the network. With CDG, multiple forwarding trees are constructed, each for aggregating a coded or compressed measurement, and these measurements are collected at the sink for recovering the uncoded transmissions from the sensors. This paper studies the problem of constructing forwarding trees for collecting and aggregating sensed data in the network under the realistic physical interference model. The problem of gathering tree construction and link scheduling is addressed jointly, through a mathematical formulation, and its complexity is underlined. Our objective is to collect data at the sink with both minimal latency and fewer transmissions. We show the joint problem is NP-hard and owing to its complexity, we present a decentralized method for solving the tree construction and the link scheduling subproblems. Our link scheduling subproblem relies on defining an interference neighbourhood for each link and co-ordinating transmissions among network links to control the interference. We prove the correctness of our algorithmic method and analyse its performance. Numerical results are presented to compare the performance of the decentralized solution with the joint model as well as prior work from the literature.

Lift–dominated pointed aircraft configurations are considered in the transonic range. To make the approximations more transparent, two–dimensionally cambered untwisted lifting wings of zero thickness with aspect ratio of order one are treated. An inner expansion, which starts as Jones's theory, is matched to a nonlinear outer transonic theory as in Cheng and Barnwell's earlier work. To clarify issues, minimize ad hoc assumptions existing in earlier studies, as well as provide a systematic expansion scheme, a deductive rather than inductive approach is used with the aid of intermediate limits and matching not documented for this problem in previous literature. High–order intermediate–limit overlap–domain representations of inner and outer expansions are derived and used to determine unknown gauge functions, coordinate scaling and other elements of the expansions. The special role of switchback terms is also described. Non–uniformities of the inner approximation associated with leading–edge singularities similar to that in incompressible thin airfoil theory are qualitatively discussed in connection with separation bubbles in a full Navier–Stokes context and interaction of boundary–layer separation and transition. Non–uniformities at the trailing edge are also discussed as well as the important role of the Kutta condition. A new expression for the dominant approximation of the wave drag due to lift is derived. The main result is that although wave drag due to lift integral has the same form as that due to thickness, the source strength of the equivalent body depends on streamwise derivatives of the lift up to a streamwise station rather than the streamwise derivative of cross–sectional area. Some examples of numerical calculations and optimization studies for different configurations are given that provide new insight on how to carry the lift with planform shaping (as one option), so that wave drag can be minimized.

The platform safety door is difficult to install in platform because the doors of railway vehicles and existing Passenger Safety doors should be alined. To be able to solve this problem, we propose the use of Rope Type Platform Safe Door (RPSD) which is a vertically retractable platform that is designed to close from top to bottom. This platform has installed safety gate pillars at intervals of 20-40 m which accommodates different types of train regardless of train length, gate opening and location. In this paper, we reviewed the application of existing PSD and RPSD in various train stops in Seoul Gyeongbu Line platform. The results of the review showed that the existing PSD may cause problem in construction, safety and cost efficiency. The use of RPSD however shows that minimal problems will be encountered.

Shortfall Risk Through Fenchel Duality

In this paper, we define a distributionally robust k-sum optimization problem as the problem of finding a solution that minimizes the worst-case expected sum of up to the k largest costs of the elements in the solution. The costs are random with a joint probability distribution that is not completely specified but rather assumed to be known to lie in a set of probability distributions. For k=1, this reduces to a distributionally robust bottleneck optimization problem while for k=n, this reduces to distributionally robust minimum sum optimization problem. Our main result is that for a Fréchet class of discrete marginal distributions with finite support, the distributionally robust k-sum combinatorial optimization problem is solvable in polynomial time if the deterministic minimum sum problem is solvable in polynomial time. This extends the result of Punnen and Aneja [On k-sum optimization, Oper. Res. Lett. 18(5)(1996), pp. 233–236] from the deterministic to the robust case. We show that this choice of the set of distributions helps preserve the submodularity of the k-sum objective function which is an useful structural property for optimization problems.

We consider the problem of makespan minimization: i.e., scheduling jobs on machines to minimize the maximum load. For the deterministic case, good approximations are known even when the machines are unrelated. However, the problem is not well-understood when there is uncertainty in the job sizes. In our setting the job sizes are stochastic, i.e., the size of a job j on machine i is a random variable Xij, whose distribution is known. (Sizes of different jobs are independent of each other.) The goal is to find a fixed assignment of jobs to machines, to minimize the expected makespan---i.e., the expected value of the maximum load over the m machines. For the identical machines special case when the size of a job is the same across all machines, a constant-factor approximation algorithm has long been known. However, the problem has remained open even for the next-harder related machines case. Our main result is a constant-factor approximation for the most general case of unrelated machines. The main technical challenge we overcome is obtaining an efficiently computable lower bound for the optimal solution. We give an exponential-sized LP that we argue gives a strong lower bound. Then we show how to round any fractional solution to satisfy only a small subset of the constraints, which are enough to bound the expected makespan of our solution. We then consider two generalizations. The first is the budgeted makespan minimization problem, where the goal is to minimize the makespan subject to scheduling any subset of jobs whose reward is at least some target reward R. We extend our above result to a constant-factor approximation here using polyhedral properties of the bipartite matching polytope. The second problem is the q-norm minimization problem, where we want to minimize the expected eq-norm of the load vectors. Here we give an O(q/ log q)-approximation algorithm using a reduction to the deterministic q-norm problem with side constraints.

The advent of executable contents such as Java applets exposes World Wide Web (WWW) users to a new class of attacks that were not possible before. Despite an array of security checking, detection, and enforcement mechanisms built into the language model, the compiler, and the run-time system of Java, serious security breach incidents due to implementation bugs still arose repeatedly in the past several years. Without a provably correct implementation of Java's security architecture specification, it is difficult to make any conclusive statements about the security characteristic of current Java virtual machines. The Spout project takes an alternative approach to address Java's security problems. Rather than attempt a provable secure implementation, we aim to confine the damages of malicious Java applets to selective machines, thus, preventing the machines behind an organization's firewall from being attacked by malicious or buggy applets. More concretely, Spout is a distributed Java execution engine that transparently decouples the processing of an incoming applet's application logic from that of graphical user interface (GUI), such that the only part of an applet that is actually running on the requesting user's host is the harmless GUI code. A unique feature of the Spout architecture that does not exist in other similar systems, is that it is completely transparent to and does not require any modifications to WWW browsers or class libraries on the end hosts. This paper describes the detailed design, implementation, and performance measurements of the first Spout prototype, which also incorporates run-time resource monitoring mechanisms to counter denial-of-service attacks.

The class Steiner minimal tree problem is an extension of the standard Steiner minimal tree problem in graphs, motivated by the problem of wire routing in the area of physical design of very large scale integration (VLSI). This problem is NP-hard, even if there are no Steiner nodes and the graph is a tree; moreover, there exists no polynomial time approximation algorithm with a constant bound on the relative error under the hypothesis that P \(\neq\) NP [16]. Hence, fast and good heuristic algorithms are needed in practice. In this paper, we present an integer programming formulation of the problem. Using Lagrangean relaxation and subgradient optimization, we derive a lower bound. In order to test the lower bound, we present a procedure for generating test problems for the class Steiner minimal tree problem that have known optimal solutions. The computational experiments for the test problems demonstrate that the lower bound is very tight and differs from the optimal solutions by only a few percent on average for sparse graphs.

For a d-dimensional random vector X, let p_{n, X}(theta ) be the probability that the convex hull of n independent copies of X contains a given point theta . We provide several sharp inequalities regarding p_{n, X}(theta ) and N_X(theta ) denoting the smallest n for which p_{n, X}(theta )ge 1/2. As a main result, we derive the totally general inequality 1/2 le alpha _X(theta )N_X(theta )le 3d + 1, where alpha _X(theta ) (a.k.a. the Tukey depth) is the minimum probability that X is in a fixed closed halfspace containing the point theta . We also show several applications of our general results: one is a moment-based bound on N_X(mathbb {E}!left[ Xright] ), which is an important quantity in randomized approaches to cubature construction or measure reduction problem. Another application is the determination of the canonical convex body included in a random convex polytope given by independent copies of X, where our combinatorial approach allows us to generalize existing results in random matrix community significantly.