Polynomial-Time Algorithms for Minimum-Time Broadcast in Trees

Abstract. This paper addresses the minimum-time broadcast problem under several modes of the line model, i.e., when long-distance calls can be placed along paths in the network. It is well known that the minimum-time broadcast problem can be solved in polynomial time under the single-port edge-disjoint paths mode. However, it is equally well known that either relaxing the model to the all-port edge-disjoint paths mode, or constraining the model to the single-port vertex-disjoint paths mode, leads to NP-complete problems; and exact solutions have been derived for specific topologies only (e.g., hypercubes or tori). In this paper we present polynomial-time algorithms for minimum-time broadcast in trees. These algorithms are obtained by application of an original technique called the merging method , which can be applied in a larger context, for instance, to solve the multicast problem or to address the restricted regimen. The merging method requires solving the minimal contention-free matrix problem whose solution presents some interest on its own.     

Polynomial-Time Decomposition Algorithms for Support Vector Machines

This paper studies the convergence properties of a general class of decomposition algorithms for support vector machines (SVMs). We provide a model algorithm for decomposition, and prove necessary and sufficient conditions for stepwise improvement of this algorithm. We introduce a simple rate certifying condition and prove a polynomial-time bound on the rate of convergence of the model algorithm when it satisfies this condition. Although it is not clear that existing SVM algorithms satisfy this condition, we provide a version of the model algorithm that does. For this algorithm we show that when the slack multiplier C satisfies 1/2 C mL, where m is the number of samples and L is a matrix norm, then it takes no more than 4LC ² m ⁴/ iterations to drive the criterion to within of its optimum.     

Polynomial-Time Algorithms for the Ordered Maximum Agreement Subtree Problem

For a set of rooted, unordered, distinctly leaf-labeled trees, the NP-hard maximum agreement subtree problem (MAST) asks for a tree contained (up to isomorphism or homeomorphism) in all of the input trees with as many labeled leaves as possible. We study the ordered variants of MAST where the trees are uniformly or non-uniformly ordered. We provide the first known polynomial-time algorithms for the uniformly and non-uniformly ordered homeomorphic variants as well as the uniformly and non-uniformly ordered isomorphic variants of MAST. Our algorithms run in time , , , and , respectively, where n is the number of leaf labels and k is the number of input trees.     

Spectral Algorithms for Unique Games

We give a new algorithm for Unique Games which is based on purely spectral techniques, in contrast to previous work in the area, which relies heavily on semidefinite programming (SDP). Given a highly satisfiable instance of Unique Games, our algorithm is able to recover a good assignment. The approximation guarantee depends only on the completeness of the game, and not on the alphabet size, while the running time depends on spectral properties of the Label-Extended graph associated with the instance of Unique Games.     

New Algorithms for Solving Simple Stochastic Games

We present new algorithms for determining optimal strategies for two-player games with proba- bilistic moves and reachability winning conditions. Such games, known as simple stochastic games, were extensively studied by A.Condon [Anne Condon. The complexity of stochastic games. Information and Computation, 96(2):203–224, 1992, Anne Condon. On algorithms for simple stochastic games. In Jin-Yi Cai, editor, Advances in Computational Complexity Theory, volume 13 of DIMACS Series in Discrete Mathematics and Theoretical Computer Science, pages 51–73. AMS, 1993]. Many interesting problems, including parity games and hence also mu-calculus model checking, can be reduced to simple stochastic games. It is an open problem, whether simple stochastic games can be solved in polynomial time. Our algorithms determine the optimal expected payoffs in the game. We use geometric interpre- tation of the search space as a subset of the hyper-cube [0,1]^N. The main idea is to divide this set into convex subregions in which linear optimization methods can be used. We show how one can proceed from one subregion to the other so that, eventually, a region containing the optinal payoffs will be found. The total number of subregions is exponential in the size of the game but, in practice, the algorithms need to visit only few of them to find a solution. We believe that our new algorithms could provide new insights into the difficult problem of deter- mining algorithmic complexity of simple stochastic games and other, equivallent problems.     

SSD数据结构与算法综述

SSD（Solid State Disk）是一种基于闪存的电可擦除可编程的新型存储器件。与普通硬盘相比,SSD具有访问延迟小、低功耗等优点。但SSD的应用也需要解决写前擦除、损耗平衡等挑战。针对这些挑战,工业界和学术界研究提出了多种复杂的算法和数据结构。对这些研究成果进行了分析和综述,同时探讨了SSD在分层存储中的应用。     

数据结构和算法的可视化教学研究与实践

本文介绍和总结了数据结构和算法的可视化ＣＡＩ软件的开发应用，并对已形成的数据结构课程的全面可视化ＣＡＩ教学模式进行了初步的探讨。     

Polynomial-Time Geometric Matching for Object Recognition

This paper considers the task of recognition and position determination, by computer, of a 2D or 3D object where the input is a single 2D brightness image, and a model of the object is known a priori. The primary contribution of this paper is a novel formulation and methods for local geometric feature matching. This formulation is based on analyzing geometric constraints on transformations of the model features which geometrically align it with a substantial subset of image features. Specifically, the formulation and algorithms for geometric feature matching presented here provide a guaranteed method for finding all feasible interpretations of the data in terms of the model. This method is robust to measurement uncertainty in the data features and to the presence of spurious scene features, and its time and space requirements are only polynomial in the size of the feature sets. This formulation provides insight into the fundamental nature of the matching problem, and the algorithms commonly used in computer vision for solving it.     

A Polynomial-Time Algorithm to Find von Neumann-Morgenstern Stable Matchings in Marriage Games

This paper considers von Neumann-Morgenstern (vNM) stable sets in marriage games. Ehlers (Journal of Economic Theory 134: 537–547, 2007) showed that if a vNM stable set exists in a marriage game, the set is a maximal distributive lattice of matchings that includes all core matchings. To determine what matchings form a vNM stable set, we propose a polynomial-time algorithm that finds a man-optimal matching and a woman-optimal matching in a vNM stable set of a given marriage game. This algorithm also generates a modified preference profile such that a vNM stable set is obtained as the core of a marriage game with the modified preference profile. It is well known that cores of marriage games are nonempty. However, the nonemptiness of cores does not imply the existence of a vNM stable set. It is proved using our algorithm that there exists a unique vNM stable set for any marriage game.     

Algorithms for the Weight Constrained Shortest Path Problem

Given a directed graph whose arcs have an associated cost, and associated weight, the weight constrained shortest path problem (WCSPP) consists of finding a least-cost path between two specified nodes, such that the total weight along the path is less than a specified value. We will consider the case of the WCSPP defined on a graph without cycles. Even in this case, the problem is NP-hard, unless all weights are equal or all costs are equal, however pseudopolynomial time algorithms are known. The WCSPP applies to a number of real-world problems. Traditionally, dynamic programming approaches were most commonly used, but in recent times other methods have been developed, including exact approaches based on Lagrangean relaxation, and fully polynomial approximation schemes. We will review the area and present a new exact algorithm, based on scaling and rounding of weights.     

Octree-Related Data Structures and Algorithms

The octree is not always a desirable data structure. Here, together with their formal definitions and related algorithms, are two data structures more suitable for graphics operations.     

Computing Optimal Attribute Weight Settings for Nearest Neighbor Algorithms

Nearest neighbor (NN) learning algorithms, examples of the lazy learning paradigm, rely on a distance function to measure the similarity of testing examples with the stored training examples. Since certain attributes are more discriminative, while others can be less or totally irrelevant, attributes should be weighed differently in the distance function. Most previous studies on weight setting for NN learning algorithms are empirical. In this paper we describe our attempt on deciding theoretically optimal weights that minimize the predictive error for NN algorithms. Assuming a uniform distribution of examples in a 2-d continuous space, we first derive the average predictive error introduced by a linear classification boundary, and then determine the optimal weight setting for any polygonal classification region. Our theoretical results of optimal attribute weights can serve as a baseline or lower bound for comparing other empirical weight setting methods.     

特定形式量化关联规则的优化挖掘

量化关联规则的挖掘是数据挖掘的一项重要任务。该文介绍了一种高效的算法,用于挖掘特定形式的量化关联规则。该算法不仅效率高而且很好地解决了区间分隔引起的规则冗余等一系列问题。最后对能够挖掘的规则形式进行了扩展。     

RNA二级结构表示方法及其转换算法

RNA二级结构的表示对研究RNA二级结构有着重要作用,该文讨论了RNA二级结构的几种表示方法,并给出了它们之间的转换算法。     

Special Issue on Memetic Algorithms

The ten papers in this special section are devoted to memetic algorithms. The papers are loosely grouped into two categories: memetic algorithm methodologies and domain-specific memetic algorithms. Briefly summarizes the articles included in this section.