38425944
Scheduling on Unrelated Machines Under Tree-Like Precedence Constraints
We present polylogarithmic approximations for the R|prec|Cmax and R|prec|∑jwjCj problems, when the precedence constraints are “treelike” – i.e., when the undirected graph underlying the precedences is a forest. We also obtain improved bounds for the weighted completion time and flow time for the case of chains with restricted assignment – this generalizes the job shop problem to these objective functions. We use the same lower bound of “congestion+dilation”, as in other job shop scheduling approaches. The first step in our algorithm for the R|prec|Cmax problem with treelike precedences involves using the algorithm of Lenstra, Shmoys and Tardos to obtain a processor assignment with the congestion + dilation value within a constant factor of the optimal. We then show how to generalize the random delays technique of Leighton, Maggs and Rao to the case of trees. For the weighted completion time, we show a certain type of reduction to the makespan problem, which dovetails well with the lower bound we employ for the makespan problem. For the special case of chains, we show a dependent rounding technique which leads to improved bounds on the weighted completion time and new bicriteria bounds for the flow time.
47278894
Equilibria in Topology Control Games for Ad Hoc Networks
We study topology control problems in ad hoc networks where network nodes get to choose their power levels in order to ensure desired connectivity properties. Unlike most other work on this topic, we assume that the network nodes are owned by different entities, whose only goal is to maximize their own utility that they get out of the network without considering the overall performance of the network. Game theory is the appropriate tool to study such selfish nodes: we define several topology control games in which the nodes need to choose power levels in order to connect to other nodes in the network to reach their communication partners while at the same time minimizing their costs. We study Nash equilibria and show that—among the games we define—these can only be guaranteed to exist if each network node is required to be connected to all other nodes (we call this the Strong Connectivity Game). For a variation called Connectivity Game, where each node is only required to be connected (possibly via intermediate nodes) to a given set of nodes, we show that Nash equilibria do not necessarily exist. We further study how to find Nash equilibria with incentive-compatible algorithms and compare the cost of Nash equilibria to the cost of a social optimum, which is a radius assignment that minimizes the total cost in a network where nodes cooperate. We also study variations of the games; one where nodes not only have to be connected, but k-connected, and one that we call the Reachability Game, where nodes have to reach as many other nodes as possible, while keeping costs low. We extend our study of the Strong Connectivity Game and the Connectivity Game to wireless networks with directional antennas and wireline networks, where nodes need to choose neighbors to which they will pay a link. Our work is a first step towards game-theoretic analyses of topology control in wireless and wireline networks.
5797236
Strong edge coloring for channel assignment in wireless radio networks
We give efficient sequential and distributed approximation algorithms for strong edge coloring graphs modeling wireless networks. Strong edge coloring is equivalent to computing a conflict-free assignment of channels or frequencies to pairwise links between transceivers in the network
14506171
Optimal constrained graph exploration
We address the problem of exploring an unknown graph <i>G</i> = (<i>V</i>, <i>E</i>) from a given start node <i>s</i> with either a tethered robot or a robot with a fuel tank of limited capacity, the former being a tighter constraint. In both variations of the problem, the robot can only move along the edges of the graph, i.e, it cannot jump between non-adjacent vertices. In the tethered robot case, if the tether (rope) has length <i>l</i>, then the robot must remain within distance <i>l</i> from the start node <i>s</i>. In the second variation, a fuel tank of limited capacity forces the robot to return to <i>s</i> after traversing <i>C</i> edges. The efficiency of algorithms for both variations of the problem is measured by the number of edges traversed during the exploration. We present an algorithm for a tethered robot which explores the graph in <i>&Ogr;</i>(¦<i>E</i>¦) edge traversals. The problem of exploration using a robot with a limited fuel tank capacity can be solved with a simple reduction from the tethered robot case and also yields a <i>&Ogr;</i>(¦<i>E</i>¦) algorithm. This improves on the previous best known bound of <i>&Ogr;</i>(¦<i>E</i>¦ + ¦<i>V</i>¦log <sup>2</sup>¦<i>V</i>¦) in [4]. Since the lower bound for the graph exploration problems is ¦<i>E</i>¦, our algorithm is optimal, thus answering the open problem of Awerbuch, Betke, Rivest, and Singh [3].
5622554
Equilibria in topology control games for ad hoc networks
We study topology control problems in ad hoc networks, where network nodes get to choose their power levels in order to ensure desired connectivity properties. Unlike most other work on this topic, we assume that the network nodes are owned by different entities, whose only goal is to maximize their own utility that they get out of the network without considering the overall performance of the network. Game theory is the appropriate tool to study such selfish nodes: we define several topology control games in which the nodes need to choose power levels in order to connect to other nodes in the network to reach their communication partners while at the same time minimizing their costs. We study Nash equilibria and show that -- among the games we define -- these can only be guaranteed to exist if all network nodes are required to be connected to all other nodes (we call this the Strong Connectivity Game). We give asymptotically tight bounds for the worst case quality of a Nash equilibrium in the Strong Connectivity Game and we improve these bounds for randomly distributed nodes. We then study the computational complexity of finding Nash equilibria and show that a polynomial-time algorithm finds Nash equilibria whose costs are at most a factor 2 off the minimum cost possible; for a variation called Connectivity Game, where each node is only required to be connected (possibly via intermediate nodes) to a given set of nodes, we show that answering the question, if a Nash equilibrium exists, is NP-hard, if the network graph satisfies the triangle inequality. For a second game called Reachability Game, where each node tries to reach as many other nodes as possible, while minimizing its radius, we show that 1+o(1)-approximate Nash equilibria exist for randomly distributed nodes. Our work is a first step towards game-theoretic analyses of ad hoc networks.
18650185
Minimization, Learning, and Conformance Testing of Boolean Programs
Boolean programs with recursion are convenient abstractions of sequential imperative programs, and can be represented as recursive state machines (RSMs) or pushdown automata. Motivated by the special structure of RSMs, we define a notion of modular visibly pushdown automata (modular VPA) and show that for the class of languages accepted by such automata, unique minimal modular VPA exist. This yields an efficient approximate minimization theorem that minimizes RSMs to within a factor of k of the minimal RSM, where k is the maximum number of parameters in any module. Using the congruence defined for minimization, we show an active learning algorithm (with a minimally adequate teacher) for context free languages in terms of modular VPAs. We also present an algorithm that constructs complete test suites for Boolean program specifications. Finally, we apply our results on learning and test generation to perform model checking of black-box Boolean programs.
45908534
KRISHNA - Concurrency Control Algorithms based on Dynamic Attributes
Three new concurrency control mechanisms that utilizes the dynamic attribute of concurrent transactions for resolving conflicts are presented. Our study shows that their performance is superior to all well-known two-phase concurrency control mechanisms. There are a large number of such algorithms but we report our findings since our approach has some unique features worth exploring.
1842716
Dynamic control of 3-D rolling contacts in two-arm manipulation
When two or more arms are used to manipulate a large object, it is necessary to maintain and control contacts between the object and effector(s) on one or more arms. The dynamic control of two arms manipulating a large object with rolling contacts is addressed. In the framework presented, the motion of the object as well as the loci of the contact points on the surface of the effectors and on the object can be directly controlled. The velocity and acceleration equations for three-dimensional rolling contacts are derived in order to obtain a dynamical model of the system. A nonlinear feedback algorithm that decouples and linearizes the system is used to demonstrate the control of rolling motion along each arm and the adaption of grasps to varying loads.<<ETX>>
32920382
Kinematic modeling of head-neck movements
The main objective is to generate kinematic models for the head and neck movements. The motivation comes from our study of individuals with quadriplegia and the need to design rehabilitation aiding devices such as robots and teletheses that can be controlled by head-neck movements. It is then necessary to develop mathematical models for the head and neck movements. Two identification methods have been applied to study the kinematics of head-neck movements of able-body as well as neck-injured subjects. In particular, sagittal plane movements are well modeled by a planar two-revolute-joint linkage. In fact, the motion in joint space seems to indicate that sagittal plane movements may be classified as a single DOF motion. Finally, a spatial three-revolute-joint system has been employed to model 3D head-neck movements.
213611
Covering rectilinear polygons with axis-parallel rectangles
We give an O( log n) factor approximation algorithm for covering a rectilinear polygon with holes using axis-parallel rectangles. This is the first polynomial time approximation algorithm for this problem with an o(log n) approximation factor. 1. Introduction. We consider the problem of covering rectilinear polygons with axis-parallel rectangles. Given a rectilinear polygon P with complexity n (complexity refers to the minimum of the number of vertical edges and the number of horizontal edges in the polygon), this problem requires determining the minimum number of axis-parallel rectangles whose union covers P. The polygon P may have holes in it. Applications. Cheng, Iyengar, and Kashyap (5) showed that this problem has applications to image compression. They claim that representing an image using a rectangle covering of its white pixels gives compression superior to that achieved by quadtrees. It also has applications to printing integrated circuits (9). Hardness. Much effort has gone into determining the computational complexity of this problem. In spite of this, the exact complexity of this problem has remained open for many years and continues to do so. Masek (19) showed that this problem is NP-complete. Later, Culberson and Reckhow (6) used a clever reduction from 3-SAT to show that this is the case even when P has no holes. The next natural question is whether the number of rectangles needed to cover P can be computed approximately. Berman and Dasgupta (2) showed that this problem is MaxSNP-Hard for polygons with holes, ruling out the possibility of a polynomial time approximation scheme. Approximation results. Note that the rectangle covering problem is a special case of the general set covering problem. Therefore, it admits an approximation algorithm with a performance guarantee of O(log n), using the greedy scheme due to Johnson (10) and Lovasz (16). This was the best approximation factor known for the rectangle covering problem until now. Further, it is known that the general set covering problem cannot be approximated any better, modulo constant terms, unless NP = P (17, 18). However, this proof of hardness assumes certain properties about the set system which do not hold for the rectangle covering problem. In this paper, we address the issue of whether the Ω(log n) approximation factor barrier can be broken in polynomial time for the rectangle covering problem. There seem to be only a few examples of nontrivial algorithms breaking this