Treewidth Lower Bounds with Brambles

In this paper we present a new technique for computing lower bounds for graph treewidth. Our technique is based on the fact that the treewidth of a graph G is the maximum order of a bramble of G minus one. We give two algorithms: one for general graphs, and one for planar graphs. The algorithm for planar graphs is shown to give a lower bound for both the treewidth and branchwidth that is at most a constant factor away from the optimum. For both algorithms, we report on extensive computational experiments that show that the algorithms often give excellent lower bounds, in particular when applied to (close to) planar graphs. This work was partially supported by the Netherlands Organisation for Scientific Research NWO (project Treewidth and Combinatorial Optimisation) and partially by the DFG research group “Algorithms, Structure, Randomness” (Grant number GR 883/9-3, GR 883/9-4).     

Upper and Lower Bounds on the Makespan of Schedules for Tree Dags on Linear Arrays

We find, in polynomial time, a schedule for a complete binary tree directed acyclic graph (dag) with n unit execution time tasks on a linear array whose makespan is optimal within a factor of 1+o(1) . Further, given a binary tree dag T with n tasks and height h , we find, in polynomial time, a schedule for T on a linear array whose makespan is optimal within a factor of 5 + o(1) . On the other hand, we prove that explicit lower and upper bounds on the makespan of optimal schedules of binary tree dags on linear arrays differ at least by a factor of 1+ . We also find, in polynomial time, schedules for bounded tree dags with n unit execution time tasks, degree d , and height on a linear array which are optimal within a factor of 1+o(1) , this time under the assumption of links with unlimited bandwidth. Finally, we compute an improved upper bound on the makespan of an optimal schedule for a tree dag on the architecture independent model of Papadimitriou and Yannakakis [14], provided that its height is not too large. Received January 21, 1997; revised June 5, 1997.     

完全图K97的边染色与4个Ramsey数的新下界

用构造性方法研究完全图K97的边的各种染色,得到4个经典Ramsey数的新下界：R（3,3,8）≥98,R（3,4,6）≥98,R（3,5,5）≥98,R（3,18）≥98。     

Lower and Upper Bounds for Linkage Discovery

For a real-valued function f defined on {0,1}n , the linkage graph of f is a hypergraph that represents the interactions among the input variables with respect to f . In this paper, lower and upper bounds for the number of function evaluations required to discover the linkage graph are rigorously analyzed in the black box scenario. First, a lower bound for discovering linkage graph is presented. To the best of our knowledge, this is the first result on the lower bound for linkage discovery. The investigation on the lower bound is based on Yao's minimax principle. For the upper bounds, a simple randomized algorithm for linkage discovery is analyzed. Based on the Kruskal-Katona theorem, we present an upper bound for discovering the linkage graph. As a corollary, we rigorously prove that O(n ²logn) function evaluations are enough for bounded functions when the number of hyperedges is O(n), which was suggested but not proven in previous works. To see the typical behavior of the algorithm for linkage discovery, three random models of fitness functions are considered. Using probabilistic methods, we prove that the number of function evaluations on the random models is generally smaller than the bound for the arbitrary case. Finally, from the relation between the linkage graph and the Walsh coefficients, it is shown that, for bounded functions, the proposed bounds are eventually the bounds for finding the Walsh coefficients.     

Lower bounds for maximal and convex layers problems

In this paper we derive tight lower bounds for the maximal and convex layers problems in the plane. Our lower bound proofs for the maxima problem and convex hull problem are simpler than those previously known. We also obtain an (nlog n) lower bound for the maximal depth problem, and the convex depth problem, when the points are given in sorted order of their x-coordinates.     

Lower Bounds for Fully Dynamic Connectivity Problems in Graphs

We prove lower bounds on the complexity of maintaining fully dynamic k -edge or k -vertex connectivity in plane graphs and in (k-1) -vertex connected graphs. We show an amortized lower bound of (log n / {k (log log n} + log b)) per edge insertion, deletion, or query operation in the cell probe model, where b is the word size of the machine and n is the number of vertices in G . We also show an amortized lower bound of (log n /(log log n + log b)) per operation for fully dynamic planarity testing in embedded graphs. These are the first lower bounds for fully dynamic connectivity problems. Received January 1995; revised February 1997.     

Upper and Lower Bounds on the Learning Curve for Gaussian Processes

In this paper we introduce and illustrate non-trivial upper and lower bounds on the learning curves for one-dimensional Guassian Processes. The analysis is carried out emphasising the effects induced on the bounds by the smoothness of the random process described by the Modified Bessel and the Squared Exponential covariance functions. We present an explanation of the early, linearly-decreasing behavior of the learning curves and the bounds as well as a study of the asymptotic behavior of the curves. The effects of the noise level and the lengthscale on the tightness of the bounds are also discussed.     

ZigBee Mesh网络路由算法改进

该文通过对ZigBee Mesh网络路由算法的研究,针对其低功耗的特点以及该网络中存在由于个别节点负荷过大而能量过早耗尽的问题,提出了一种改进的路由算法。以达到减少网络开销,降低网络功耗,延长网络寿命,提高网络性能的目的。     

Bounds on tradeoffs between randomness and communication complexity

The power of randomness in improving the efficiency (or even possibility) of computations has been demonstrated in numerous contexts. A fundamental question ishow much randomness is required for these improvements, or how does the improvement grow as a function of the amount of randomness allowed. This quantitative question, restricted to the context of communication complexity, is the focus of our paper.We prove general lower bounds on the amount of randomness used in randomized protocols for computing a functionf, the input of which is split between two parties. The bounds depend on the number of bits communicated and the deterministic communication complexity off. Four models for communication complexity are considered: the random input of the parties may be public or private, and the communication may be one-way or two-way. (Unbounded advantage is allowed.)The bounds are shown to be tight; i.e., we demonstrate functions and protocols for these functions which meet the above bounds up to a constant factor. We do this for all the models, for all values of the deterministic communication complexity, and for all possible quantities of bits communicated.     

一种矩形网格自动剖分及加密算法

利用差分算子分列式进行高效预处理,需要对目标域进行矩形网格剖分。而常用的有限元网格自动生成器难以满足需要。文章吸取了逐点比较法的思想,设计了一种新的算法,可以实现矩形网格的均匀和非均匀剖分以及网格的自动加密,并大大简化剖分时的运算量和需要记录的数据量。     

A Note on Parallel Selection on Coarse-Grained Multicomputers

Consider the selection problem of determining the k th smallest element of a set of n elements. Under the CGM (coarse-grained multicomputer) model with p processors and O(n/p) local memory, we present a deterministic parallel algorithm for the selection problem that requires O( log p) communication rounds. Besides requiring a low number of communication rounds, the algorithm also attempts to minimize the total amount of data transmitted in each round (only O(p) except in the last round). In addition to showing theoretical complexities, we present very promising experimental results obtained on a parallel machine that show almost linear speedup, indicating the efficiency and scalability of the proposed algorithm. Received June 1, 1997; revised March 10, 1998.     

Lower and upper bounds for the mixed capacitated arc routing problem

This paper presents a linear formulation, valid inequalities, and a lower bounding procedure for the mixed capacitated arc routing problem (MCARP). Moreover, three constructive heuristics and a memetic algorithm are described. Lower and upper bounds have been compared on two sets of randomly generated instances. Computational results show that the average gaps between lower and upper bounds are 0.51% and 0.33%, respectively.     

Upper and Lower Bounds for Randomized Search Heuristics in Black-Box Optimization

Randomized search heuristics like local search, tabu search, simulated annealing, or all kinds of evolutionary algorithms have many applications. However, for most problems the best worst-case expected run times are achieved by more problem-specific algorithms. This raises the question about the limits of general randomized search heuristics. Here a framework called black-box optimization is developed. The essential issue is that the problem but not the problem instance is knownto the algorithm which can collect information about the instance only by asking for the value of points in the search space. All known randomized search heuristics fit into this scenario. Lower bounds on the black-box complexity of problems are derived without complexity theoretical assumptions and are compared with upper bounds in this scenario.     

Lower Bounds for Dynamic Tree Embedding in Bipartite Networks

There are many parallel computations that are tree structured. The structure of a tree is usually unpredictable at compiler-time; the tree grows gradually during the course of a computation. The dynamic tree embedding problem is to distribute the processes of a parallel computation over processors in a parallel computer such that processors perform roughly the same amount of computation, and that communicating processes are assigned to processors that are close to each other. In this paper, we establish lower bounds for the performance ratio of dynamic tree embedding in bipartite static networks, including numerous important networks such asn-dimensional meshes,n-dimensional tori,k-aryn-cubes, cube-connected cycles, and butterflies. Our lower bounds are obtained from both tree and network properties and are applicable to a general class of dynamic tree embedding algorithms.     

IEEE 802.16 Mesh模式下基于QoS的时隙分配算法

IEEE 802.16-2004标准定义了Mesh模式下的调度机制，基于这些调度机制下的数据信道资源分配算法，在标准中没有详细规定。该文提出了两种基于优先级的时隙分配算法，以实现MAC层的QoS，通过仿真分析了平均分组延迟、请求失败率和时隙利用率。仿真结果表明这些算法实现了对不同需求的业务流的QoS保障。     

Lower and Upper Bounds on FIFO Buffer Management in QoS Switches

We consider the management of FIFO buffers for network switches providing differentiated services. In each time step, an arbitrary number of packets arrive and only one packet can be sent. The buffer can store a limited number of packets and, due to the FIFO property, the sequence of sent packets has to be a subsequence of the arriving packets. The differentiated service model is abstracted by attributing each packet with a value according to its service level. A buffer management strategy can drop packets, and the goal is to maximize the sum of the values of sent packets. For only two different packet values, we introduce the account strategy and prove that this strategy achieves an optimal competitive ratio of if the buffer size tends to infinity and an optimal competitive ratio of for arbitrary buffer sizes. For general packet values, the simple preemptive greedy strategy (PG) is studied. We show that PG achieves a competitive ratio of which is the best known upper bound on the competitive ratio of this problem. In addition, we give a lower bound of on the competitive ratio of PG which improves the previously known lower bound. As a consequence, the competitive ratio of PG cannot be further improved significantly. Supported by the DFG grant WE 2842/1. A preliminary version of this paper appeared in Proceedings of the 14th Annual European Symposium on Algorithms (ESA), 2006.     

有限域与Ramsey数Rn(k)的下界

研究有限域GF(p')上的循环图的结构性质,给出一些图的团数的解析表达式,并给出计算Rarnsey数Rn(k)下界的一种算法,得到一个Ramsey数的新下界：R3(8)≥4111。     

BLE Mesh组网的可穿戴设备低功耗研究

针对目前可穿戴式设备功耗高的问题,本文进行了基于BLE Mesh组网的可穿戴设备低功耗的研究.以可穿戴单兵冲击波损伤测评系统为例,设计了一款基于Mesh组网的单兵冲击波损伤测评系统,该系统在原有系统的基础上增加了一个蓝牙组网.由于可穿戴设备采用纽扣电池供电,为了保证该系统的功耗不能有大幅度的增加,本文采用泛洪算法和低功...     

Lower Bounds for Dynamic Data Structures on Algebraic RAMs

Abstract. In a seminal paper of 1989, Fredman and Saks proved lower bounds for some important data-structure problems in the cell probe model. This model assumes that data structures are stored in memory with a known word length. In this paper we consider random access machines (RAMs) that can add, subtract, compare, multiply and divide integer or real numbers, with no size limitation. These are referred to as algebraic RAMs . We prove new lower bounds for two important data-structure problems, union-find and dynamic prefix sums . To this end we apply the generalized Fredman—Saks technique introduced by the authors in a previous paper. The generalized technique relies on a certain well-defined function, Output Variability , that characterizes in some sense the power of the computational model. Fredman and Saks' work implied bounds on output variability for the cell probe model; in this paper we provide the first bounds for algebraic RAMs, and show that they suffice for proving tight lower bounds for useful problems. An important feature of the problems we consider is that in a data structure of size n , the data stored are members of {0,ldots,n} . This makes the derivation of lower bounds for such problems on a RAM without word-size limitations a particular challenge; previous RAM lower bounds we are aware of depend on the fact that the data for the computation can vary over a large domain.     

Lower Bounds on Learning Decision Lists and Trees

k-Decision lists and decision trees play important roles in learning theory as well as in practical learning systems.k-Decision lists generalize classes such as monomials,k-DNF, andk-CNF, and like these subclasses they are polynomially PAC-learnable [R. Rivest,Mach. Learning2(1987), 229–246]. This leaves open the question of whetherk-decision lists can be learned as efficiently ask-DNF. We answer this question negatively in a certain sense, thus disproving a claim in a popular textbook [M. Anthony and N. Biggs, “Computational Learning Theory,” Cambridge Univ. Press, Cambridge, UK, 1992]. Decision trees, on the other hand, are not even known to be polynomially PAC-learnable, despite their widespread practical application. We will show that decision trees are not likely to be efficiently PAC-learnable. We summarize our specific results. The following problems cannot be approximated in polynomial time within a factor of 2^{logδ n}for anyδ<1, unlessNP⊂DTIME[2^{polylog n}]: a generalized set cover,k-decision lists,k-decision lists by monotone decision lists, and decision trees. Decision lists cannot be approximated in polynomial time within a factor ofn^δ, for some constantδ>0, unlessNP=P. Also,k-decision lists withl0–1 alternations cannot be approximated within a factor log^l nunlessNP⊂DTIME[n^{O(log log n)}] (providing an interesting comparison to the upper bound obtained by A. Dhagat and L. Hellerstein [in“FOCS '94,” pp. 64–74]).