Stochastic Mean Payoff Games: Smoothed Analysis and Approximation Schemes

We consider two-person zero-sum stochastic mean payoff games with perfect information, or BWR-games, given by a digraph G=(V, E), with local rewards r: E→ℝ, and three types of vertices: black VB, white VW, and random VR forming a partition of V. It is a long-standing open question whether a polynomial time algorithm for BWR-games exists, or not. In fact, a pseudo-polynomial algorithm for these games would already imply their polynomial solvability. In this paper, we show that BWR-games with a constant number of random nodes can be solved in pseudo-polynomial time. That is, for any such game with a few random nodes |VR|=O(1), a saddle point in pure stationary strategies can be found in time polynomial in |VW|+|VB|, the maximum absolute local reward R, and the common denominator of the transition probabilities.

We consider some well-known families of two-player zero-sum perfect-information stochastic games played on finite directed graphs. The families include stochastic parity games, stochastic mean payoff games, and simple stochastic games. We show that the tasks of solving games in each of these classes (quantitiatively or strategically) are all polynomial time equivalent. In addition, we exhibit a linear time algorithm that given a simple stochastic game and the values of all positions of that game, computes a pair of optimal strategies.

We postulate that surgical sampling and pathologic evaluation of lymph nodes of surgical specimens from patients with stage I non-small-cell lung cancer (NSCLC) can have an effect on the time to recurrence and survival of these patients. We analyzed data on 442 patients with stage I NSCLC who were treated with surgical resection and some form of lymph node sampling. Associations between total lymph nodes sampled and disease-free survival (DFS) and overall survival (OS) were investigated. The effect of total lymph node stations sampled and the surgical techniques (random lymph node sampling, systematic sampling [SS], or complete mediastinal lymph node dissection [MLND]) on DFS and OS was also studied. Complete MLND and SS were defined as dissection or sampling of levels 4, 7, and 10 for right-sided lesions and levels 5 or 6 and 7 for left-sided lesions. Patients were divided into quartiles on the basis of total number of lymph nodes sampled. Improved DFS and OS were associated with greater number of lymph nodes sampled. SS and MLND were associated with improved survival compared with random lymph node sampling. The total number of lymph nodes sampled maintained strong significance in the multivariate analysis. These results indicate that examining a greater number of lymph nodes in patients with stage I NSCLC treated with resection increases the likelihood of proper staging and affects patient outcome. Such information is important not only for therapy and prognosis of individuals but also for identifying those who may benefit from adjuvant therapy.

In view of the deficiency of the traditional RRT algorithm parameters setting, a fuzzy adaptive RRT algorithm is proposed based on the analysis of RRT realization mechanism. According to the number of random nodes and the total nodes in tree, a fuzzy inference system is designed, which can adaptive update selection probability g p and step length  . Chaotic sequence is adopted to generate initial random node position. The simulation results show that new strategy can set parameters more reasonable; improve the efficiency and the success rate obvious, especially for complex task environment.

We present exact analytical results for the degree distribution in a directed network model that grows by node duplication (ND). Such models are useful in the study of the structure and growth dynamics of gene regulatory networks and scientific citation networks. Starting from an initial seed network, at each time step a random node, referred to as a mother node, is selected for duplication. Its daughter node is added to the network and duplicates each outgoing link of the mother node with probability p . In addition, the daughter node forms a directed link to the mother node itself. Thus, the model is referred to as the corded directed-node-duplication (DND) model. The corresponding undirected ND model was studied before and was found to exhibit a power-law degree distribution. We obtain analytical results for the in-degree distribution , and for the out-degree distribution , of the corded DND network at time t. It is found that the in-degrees follow a shifted power-law distribution, so the network is asymptotically scale free. In contrast, the out-degree distribution is a narrow distribution, that converges to a Poisson distribution in the limit of and to a Gaussian distribution in the limit of . Such distinction between a broad in-degree distribution and a narrow out-degree distribution is common in empirical networks such as scientific citation networks. Using these distributions we calculate the mean degree , which converges to in the large network limit, for the whole range of 0 < p < 1. This is in contrast to the corresponding undirected network, which exhibits a phase transition at p = 1/2 such that for p > 1/2 the mean degree diverges in the large network limit. We also present analytical results for the distribution of the number of upstream nodes, , and for the distribution of the number of downstream nodes, , from a random node. We show that the mean values scale logarithmically with the network size. This means that in the large network limit only a diminishing fraction of pairs of nodes are connected by directed paths, unlike the corded undirected ND network that consists of a single connected component. Therefore, the corded DND network is not a small-world network.

Several algorithms have proven to be useful in computing the shortest path between two nodes in a network. Their complexity depends on the problem definition and size of the network measured by the total number of nodes N. In these algorithms, finding all the shortest paths from a fixed node is a computation of complexity O(N x N). These algorithms have been used successfully in long-haul networks for many years. Recent growth of such networks to large numbers of nodes (e.g., N > 500) demands a more efficient approach. This paper develops three heuristics based on measured topological characteristics of computer communication networks and applies them in the construction of faster algorithms. Determination of the shortest path between two random nodes is then shown to require 50 to 60% less computation.

There is a graph G = (V, E), which has n vertices and l edges. Color the vertices of G black or white, ensuring no black vertex is adjacent to any white vertex, thus partitioning them into disjoint black and white sets. The optimal solution of the black and white coloring (BWC) problem is defined as the coloring scheme that maximizes the number of white vertices in the corresponding set, given a fixed number of black vertices. This problem is a NP-complete problem, widely used in reagent product storage in chemical industry and the solution to the problem of black and white queens in chess. The paper presents a swarm evolution algorithm based on improved simulated annealing search and evolutionary operation with probability learning mechanism. Furthermore, crossover operation, perturbation operation, and tabu search strategy improve the search ability of the algorithm, while evolutionary operation with probability learning mechanism increases the probability of the algorithm finding better solutions. Using Cayley graphs, random graphs, semi-random graphs, and benchmark DIMACS graphs, experiments are conducted to compare the finding results from swarm evolution algorithm and other classical heuristic algorithms. Experimental results show that the swarm evolution algorithm outperforms other heuristic algorithms in solving the BWC problem, and the swarm evolution algorithm can improve the known best results of the BWC problem.

Policy controlled self-configuration in unattended wireless sensor networks

In pervasive computing environments, it is often required to cover a certain service area by a given deployment of nodes or access points. In case of large inaccessible areas, often the node deployment is random. In this paper, given a random uniform node distribution over a 2-D region, we propose a simple distributed solution for self-organized node placement to satisfy coverage of the given region of interest using least number of active nodes. We assume that the nodes are identical and each of them covers a circular area. To ensure coverage we tessellate the area with regular hexagons, and attempt to place a node at each vertex and the center of each hexagon termed as target points. By the proposed distributed algorithm, unique nodes are selected to fill up the target points mutually exclusively with limited displacement. Analysis and simulation studies show that proposed algorithm with less neighborhood information and simpler computation solves the coverage problem using minimum number of active nodes, and with minimum displacement in 95 % cases. Also, the process terminates in constant number of rounds only.

This paper presents a new approach to solving large-scale Markov decision processes (MDP) which uses simulation to generate empirical estimates of the parameters for an approximating MDP model. We begin with a brief description of this simulation for model generation algorithm and discuss some theoretical concerns regarding its implementation. We then discuss the application of the approach to a problem of choosing the optimal routes for calls within a telephone network. Although an MDP approach to this problem has been shown to be effective on small problems, no optimal procedure has yet been developed for solving this problem when the network has a nontrivial number of nodes. The ability of the algorithm to handle the complexity of such larger networks is demonstrated through some experimental results, and a comparison of its relative performance with respect to several existing solution methodologies is provided.

In this paper we study group distributed key management schemes for wireless sensor networks. We focus on forward secrecy and backward secrecy which means protecting the group keys used in the past and to be used in the future against an adversary who has gained accesses to the network. Unfortunately, most existing distributed schemes for group key management do not guarantee forward and backward secrecy when a certain number of nodes are compromised or some group keys are leaked. In this paper, we propose a new dynamic distributed group key management scheme based on local collaboration that provides both forward and backward secrecy. Also we prove its robustness against various node capture attacks and compare it with two related schemes both analytically and by simulations to verify its efficiency on storage and communication overhead.

The relative value iteration scheme (RVI) for Markov decision processes (MDP) dates back to White (1963) , a seminal work, which introduced an algorithm for solving the ergodic dynamic programming equation for the finite state, finite action case. Its ramifications have given rise to popular learning algorithms (Q-learning). More recently, this algorithm gained prominence because of its implications for model predictive control (MPC). For stochastic control problems on an infinite time horizon, especially for problems that seek to optimize the average performance (ergodic control), obtaining the optimal policy in explicit form is only possible for a few classes of well-structured models. What is often used in practice is a heuristic method called the rolling horizon, or receding horizon, or MPC. This works as follows: one solves the finite horizon problem for a given number of steps N, or for an interval [0,T] in the case of a continuous time problem. The result is a nonstationary Markov policy, which is optimal for the finite horizon problem. We fix the initial action (this is the action determined at the Nth step of the value iteration (VI) algorithm) and apply it as a stationary Markov control. We refer to this Markov control as the rolling horizon control. This of course depends on the length of the horizon N. One expects that for well-structured problems, if N is sufficiently large, then the rolling horizon control is near optimal. Of course, this is a heuristic. The rolling horizon control might not even be stable. For a good discussion on this problem, we refer the reader to Della Vecchia et al. (2012) . Obtaining such solutions is further complicated by the fact that the value of the ergodic cost required in the successive iteration scheme is not known. This is the reason for the RVI.

Query answering over inconsistent knowledge bases: A probabilistic approach

A note on the approximation of mean-payoff games

The black and white traveling salesman problem (BWTSP) is to find the minimum cost hamiltonian tour of an undirected complete graph G, containing black and white vertices, subject to two restrictions: the number of white vertices, and the cost of the subtour between two consecutive black vertices are bounded. This paper focuses on designing approximation algorithms for the BWTSP in a graph satisfying the triangle inequality. We show that approximating the tour which satisfies the length constraint is NP-hard. We then show that the BWTSP can be approximated with tour cost (4 - 3/2Q) times the optimal cost, when at most Q white vertices appear between two consecutive black vertices. When exactly Q white vertices appear between two consecutive black vertices, the approximation bound can be slightly improved to (4- 15/8Q). This approximation bound is further improved to 2.5 when Q = 2.