A 2-approximation algorithm for the zookeeper's problem

Algorithms for Computing Motorcycle Graphs Lie Yan We present a new algorithm for computing motorcycle graphs that runs inO(n) time for any e > 0, improving on all previously known algorithms. If the motorcycles follow only C different directions, our algorithm can be made to run in O(Cn log n) time. The main application of this result is to computing the straight skeleton of a polygon. It allows us to compute the straight skeleton of a non-degenerate polygon with h holes in O(n √ h+ 1 log n+n) expected time. If all input coordinates are O(log n)-bit rational numbers, we can compute the straight skeleton of a (possibly degenerate) polygon with h holes in O(n √ h+ 1 log n) expected time. In particular, it means that we can compute the straight skeleton of a simple polygon in O(n log n) expected time if all input coordinates areO(log n)-bit rationals, while all previously known algorithms have worst-case running time ω(n).

We propose a unifying framework based on configuration linear programs and randomized rounding, for different energy optimization problems in the dynamic speed-scaling setting. We apply our framework to various scheduling and routing problems in heterogeneous computing and networking environments. We first consider the energy minimization problem of scheduling a set of jobs on a set of parallel speed-scalable processors in a fully heterogeneous setting. For both the preemptive-non-migratory and the preemptive-migratory variants, our approach allows us to obtain solutions of almost the same quality as for the homogeneous environment. By exploiting the result for the preemptive-non-migratory variant, we are able to improve the best known approximation ratio for the single processor non-preemptive problem. Furthermore, we show that our approach allows to obtain a constant-factor approximation algorithm for the power-aware preemptive job shop scheduling problem. Finally, we consider the min-power routing problem where we are given a network modeled by an undirected graph and a set of uniform demands that have to be routed on integral routes from their sources to their destinations so that the energy consumption is minimized. We improve the best known approximation ratio for this problem.

Parallel algorithms are given for the exact solution of the hidden-line problem. Most of the parallel algorithms proposed for visibility problems in the literature give approximate solutions. and thus cannot yield an upper bound on the complexity of the particular problem. The first algorithm proposed here is worth mentioning not only for its simplicity. but also from a practical point of view: a speed up of a factor P is achieved by using P processors. 1≤P≤N, where N is the number of edges used to describe a polygonal scene. Additionally. the problem of aliasing inherent with approximation methods is avoided. The significance of the second algorithm, which is based on the first one, is mainly on the theoretical level: it is used to establish the parallel complexity of the hidden-line problem. The sequential complexity of this problem has recently been proved to be Θ(N2), and now we can prove that in the parallel case the problem is in the complexity class NC, i.e., it can be solved in time polynomial in log N by using a number of processors polynomial in N, assuming any reasonable model of parallel computation. More particularly, an O (log N) parallel time solution is given which cannot be further improved even if arbitrarily many processors of a concurrent read, exclusive write parallel RAM model are available.

A 2-approximation algorithm for the zookeeper's problem

We present a hybrid approach to generate plausible motions for high-DOF human-like articulated figures in constrained environment with multiple obstacles. The method combines motion planning and motion blending techniques to efficiently produce natural and collision-free human motion for different tasks.

Algorithms for line clipping against convex polygon have been studied for a long time and many research papers have been published so far. In spite of the latest graphical hardware development and significant increase of performance the clipping is still a bottleneck of the graphical pipeline. This paper presents a new robust and fast algorithm for line clipping by a convex polygon. The algorithm uses a small preprocessing in order to obtain significant speed up. The proposed algorithm is especially convenient for applications where points or lines are represented in homogeneous coordinates. The algorithm does not use division in floating point representation as the resulting points are in homogeneous coordinates. The algorithms benefit if vector-vector hardware supported operations can be used

The routing problem is one of the studied transportation problems. In the paper the communication networks routing problem is presented. This problem is an example of mulitcriteria optimization problem which the solution is the set of non–dominated solutions. Four algorithms for determination routes belong to the set of non–dominated solutions are shown. Additionally, other routing problems that have been researched by staff of the Institute of Informatics are discussed.

Today’s customer-driven economic environment shifts from “supply chain” to “demand chain”. To successfully compete, companies are faced with the challenge of minimizing inventory and reducing warehouse costs whenever possible while keeping retailers’ shelves full. Cross Docking is a strategy whose ability to reduce lead times, control inventory carrying costs and deliver just-in-time service with a minimal investment makes it an attractive option for many companies responding to economic pressures. In a cross docking strategy, warehouses and distribution centers serve as transfer points for inventory, but no inventory is held at these transfer points. One of the keys to keeping a Cross Docking facility synchronized is to design a system and schedule that are obtainable, taking into account travel times and expectations for how much freight will actually fit on a truck; therefore, Vehicle Routing should be considered. This research examines a Vehicle Routing Problem with Cross Docking (VRPCD) considering cross docking operational characteristics such as assignment restrictions, deadlines and door environment. A sequential operational VRPCD model is presented. Its objective is to determine the best route that minimizes operational costs of shipment, and the minimum operational cost within the cross docking facility. A two-phase algorithm using Variable Neighborhood Search (VNS) has been proposed. The experimental results show that the VNS algorithm is capable of finding good solutions in a much shorter computation time when compared with Gurobi Optimizer solutions. Good quality of solutions is obtained in all the experiments developed.

We study the problem of computing constrained shortest paths for battery electric vehicles. Since battery capacities are limited, fastest routes are often infeasible. Instead, users are interested in fast routes where the energy consumption does not exceed the battery capacity. For that, drivers can deliberately reduce speed to save energy. Hence, route planning should provide both path and speed recommendations. To tackle the resulting NP-hard optimization problem, previous work trades correctness or accuracy of the underlying model for practical running times. In this work, we present a novel framework to compute optimal constrained shortest paths for electric vehicles that uses more realistic physical models, while taking speed adaptation into account. Careful algorithm engineering makes the approach practical even on large, realistic road networks: We compute optimal solutions in less than a second for typical battery capacities, matching performance of previous inexact methods. For even faster performance, the approach can easily be extended with heuristics that provide high quality solutions within milliseconds.

The dominating set problem asks for a small subset D of nodes in a graph such that every node is either in D or adjacent to a node in D. This problem arises in a number of distributed network applications, where it is important to locate a small number of centers in the network such that every node is nearby at least one center. Finding a dominating set of minimum size is NP-complete, and the best known approximation is logarithmic in the maximum degree of the graph and is provided by the same simple greedy approach that gives the well-known logarithmic approximation result for the closely related set cover problem.We describe and analyze new randomized distributed algorithms for the dominating set problem that run in polylogarithmic time, independent of the diameter of the network, and that return a dominating set of size within a logarithmic factor from optimal, with high probability. In particular, our best algorithm runs in O(log n log Δ) rounds with high probability, where n is the number of nodes, Δ is one plus the maximum degree of any node, and each round involves a constant number of message exchanges among any two neighbors; the size of the dominating set obtained is within O (log Δ) of the optimal in expectation and within O(log n) of the optimal with high probability. We also describe generalizations to the weighted case and the case of multiple covering requirements.

At first thought, one may not realize the need for a special issue of Parallel and Distributed Computing Practices focused on Cluster Computing when our community has already invested years of research and spent a wealth of resources on traditional Big Iron supercomputers, for instance, the SGI/Cray Origin and IBM SP. Academia, industry, and national laboratories are still using, and for the foreseeable future, will continue to use, supercomputers to solve both grand-challenge scale and high-throughput applications. Then why the interest and new popularity of research into clusters for high-performance parallel and distributed applications? Clusters incorporate the tremendous successes that are attributable to our parallel and distributed processing community. Over the next decade, clusters will span the entire range of high-performance computing platforms. Instead of being restricted solely to supercomputers for achieving high-performance computing, the spectrum of available platforms will spread out to Beowulf-class clusters, to superclusters, and on to supercomputers. Moving along this continuum represents increasing computational resources, which in turn allows the capability for solving larger classes of applications or instances of problems. Compute-bound applications on workstations often may take advantage of the extra horsepower provided by symmetric multiprocessors. Applications with even larger computational requirements and a high-degree of concurrency may use Beowulf clusters, that is, clusters that are home-built from mass-market, commercial off-the-shelf workstations and networks, for instance, PC's interconnected by Fast Ethernet. A supercluster may contain commodity SMP nodes interconnected with scalable, low-latency, high-bandwidth networks, and is integrated by a system vendor rather than the computational scientist. Applications with greater complexity, for example, grand challenges from the sciences, demand scalable systems with high-performance, interconnects, perhaps coupled with terascale I/O subsystems, and thus, are appropriate for these superclusters. Finally, supercomputers, the largest of the clusters, may provide the ultimate platform for the highest-fidelity models and simulations and data-intensive applications. At each step up this ladder of cluster architectures, the system cost increases approximately by an order of magnitude, but having the high-performance capability to solve the problem of interest may require an entry point at any of these levels, the Beowulf, or supercluster, or even supercomputer platform. Cluster computing with Beowulf- or superclusters, thus, may be one or two orders of magnitude less expensive than a supercomputer, and provide a cost-effective solution and capability that was not available on a workstation. But this cost comparison measures just the basic system price. What about the applications? As recently as a few years ago, the lack of a canonical high-performance architectural paradigm meant that migrating to a new computer system, even from the same vendor, typically required redesigning applications to efficiently use the high-performance system. Thus, the application must be redesigned with parallel algorithms and libraries that are optimized for each high-performance system. This process of porting, redesigning, optimizing, debugging, and analyzing, the application may in fact be prohibitively expensive, and certainly frustrating when the process is completed just in time to greet the next generation system! That was then, this is now. With the successful standardization of system-level interfaces, many of these issues no longer hinder our expedited use of these new, high-performance clusters. The message-passing interface (MPI) is a clear example of a standard that has contributed significantly to the success of cluster computing. Supercomputer vendors working together with the high-performance computing community embarked on a process to standardize the user-level interface and behavior for passing messages between concurrent tasks. Now, using ordinary sequential compilers and vendor-supplied or freely-available implementations of this message-passing interface, applications can be implemented efficiently on one supercomputer and ported with little or no effort to other parallel machines. The message-passing paradigm, thus, provides a reasonably good canonical high-performance model and methodology for implementing high-performance applications. An algorithm that exhibits efficient execution and scaling on one machine then is likely to perform well on another with little or no additional programming effort. Using this cluster computing paradigm, algorithms typically are optimized by minimizing the number of remote memory accesses (reducing the amount of messages passed), and carefully organizing the data placement to increase memory locality. Thus, high-performance algorithms and applications that have been optimized for supercomputers, using the same cluster paradigm, may be appropriate for Beowulf and superclusters. Cluster computing, realizing the importance of a standard high-performance programming environment that applies equally well to both ends of the architectural spectrum, highly leverages these and other successes from parallel and distributed processing research and development. This is in an exciting, new era for high-performance computing where the canonical architectural paradigm stretches from home-built Beowulf clusters, to superclusters, and on to supercomputers. But cluster computing faces some challenges ahead of it. Continued research is required for designing 1) scalable, high-performance algorithms, applications, and methodologies, that can tolerate the communication overheads, and adapt to hybrid, SMP, and heterogeneous, nodes; 2) high-performance computer architectures, scalable interconnection networks, and I/O subsystems; and 3) scalable systems software, compilers, and monitoring tools. Cluster computing has come of age, and it is high time for the parallel and distributed processing community to lay the groundwork for our own legacy of success stories. David A. Bader University of New Mexico

Polygonal models are ubiquitous in computer graphics but their real time manipulation and rendering especially in interactive application environments have become a threat because of their huge sizes and complexity. A whole family of automatic algorithms emerged during the last decade to help out this problem, but they reduce the complexity of the models uniformly without caring about semantic importance of localized parts of a mesh. Only a few algorithms deal with adaptive simplification of polygonal models. We propose a new model for user-driven simplification exploiting the simplification hierarchy and hypertriangulation model [P. Cignoni et al.] that lends a user the most of the functionalities of existing adaptive simplification algorithms in one place and is quite simple to implement. The proposed new underlying data structures are compact and support real time navigation across continuous LODs of a model; any desirable LOD can be extracted efficiently and can further be fine-tuned. The proposed model for adaptive simplification supports two key operations for selective refinement and selective simplification; their effect has been shown on various polygonal models. Comparison with related work shows that the proposed model provides combined environment at reduced overhead of memory space usage and faster running times.

We consider computing a longest palindrome in the streaming model, where the symbols arrive one-by-one and we do not have random access to the input. While computing the answer exactly using sublinear space is not possible in such a setting, one can still hope for a good approximation guarantee. Our contribution is twofold. First, we provide lower bounds on the space requirements for randomized approximation algorithms processing inputs of length n. We rule out Las Vegas algorithms, as they cannot achieve sublinear space complexity. For Monte Carlo algorithms, we prove a lower bounds of Omega(M log min {|Sigma|, M}) bits of memory; here M=n/E for approximating the answer with additive error E, and M= log n / log (1 + epsilon) for approximating the answer with multiplicative error (1 + epsilon). Second, we design three real-time algorithms for this problem. Our Monte Carlo approximation algorithms for both additive and multiplicative versions of the problem use O(M) words of memory. Thus the obtained lower bounds are asymptotically tight up to a logarithmic factor. The third algorithm is deterministic and finds a longest palindrome exactly if it is short. This algorithm can be run in parallel with a Monte Carlo algorithm to obtain better results in practice. Overall, both the time and space complexity of finding a longest palindrome in a stream are essentially settled.

Application of a Derivative-Free Method with Projection Skill to Solve an Optimization Problem

Non-convex contour reconstruction