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Approximation algorithms for optimal decision trees and adaptive TSP problems

by Anupam Gupta, Ravishankar Krishnaswamy, Viswanath Nagarajan, R. Ravi , 2010
"... ..."
Abstract - Cited by 18 (4 self) - Add to MetaCart
Abstract not found

The parti-game algorithm for variable resolution reinforcement learning in multidimensional state-spaces

by Andrew W. Moore, Christopher G. Atkeson - MACHINE LEARNING , 1995
"... Parti-game is a new algorithm for learning feasible trajectories to goal regions in high dimensional continuous state-spaces. In high dimensions it is essential that learning does not plan uniformly over a state-space. Parti-game maintains a decision-tree partitioning of state-space and applies tec ..."
Abstract - Cited by 255 (9 self) - Add to MetaCart
Parti-game is a new algorithm for learning feasible trajectories to goal regions in high dimensional continuous state-spaces. In high dimensions it is essential that learning does not plan uniformly over a state-space. Parti-game maintains a decision-tree partitioning of state-space and applies

Boosted sampling: Approximation algorithms for stochastic optimization problems

by Anupam Gupta, Martin Pál, R. Ravi, Amitabh Sinha - IN: 36TH STOC , 2004
"... Several combinatorial optimization problems choose elements to minimize the total cost of constructing a feasible solution that satisfies requirements of clients. In the STEINER TREE problem, for example, edges must be chosen to connect terminals (clients); in VERTEX COVER, vertices must be chosen t ..."
Abstract - Cited by 98 (23 self) - Add to MetaCart
factor of σ> 1. The goal is to minimize the first stage cost plus the expected second stage cost. We give a general yet simple technique to adapt approximation algorithms for several deterministic problems to their stochastic versions via the following method. • First stage: Draw σ independent sets

Approximating TSP Solution by MST Based Graph Pyramid

by Yll Haxhimusa, Walterg. Kropatsch, Andreas Lehrbaum, et al. , 2007
"... The traveling salesperson problem (TSP) is difficult to solve for input instances with large number of cities. Instead of finding the solution of an input with a large number of cities, the problem is approximated into a simpler form containing smaller number of cities, which is then solved optimal ..."
Abstract - Cited by 4 (2 self) - Add to MetaCart
the optimal solution. Expanding this tour solution in a top-down manner to the lower levels of the pyramid approximates the solution. The new model has an adaptive spatial structure and it simulates visual acuity and visual attention. The model solves the TSP problem sequentially, by moving attention from

Optimal Approximation Algorithms for Multi-agent Combinatorial Problems with Discounted Price Functions

by Gagan Goel, Pushkar Tripathi, Lei Wang
"... Submodular functions are an important class of functions in combinatorial optimization which satisfy the natural properties of decreasing marginal costs. The study of these functions has led to strong structural properties with applications in many areas. Recently, there has been significant interes ..."
Abstract - Cited by 3 (1 self) - Add to MetaCart
interest in extending the theory of algorithms for optimizing combinatorial problems (such as network design problem of spanning tree) over submodular functions. Unfortunately, the lower bounds under the general class of submodular functions are known to be very high for many of the classical problems

Static Optimality and Dynamic Search-Optimality in Lists and Trees

by Avrim Blum, Shuchi Chawla, Adam Kalai , 2002
"... Adaptive data structures form a central topic of online algorithms research, beginning with the results of Sleator and Tarjan showing that splay trees achieve static optimality for search trees, and that Move-toFront is constant competitive for the list update prob- lem [ST85a, ST85b]. This paper is ..."
Abstract - Cited by 26 (3 self) - Add to MetaCart
Adaptive data structures form a central topic of online algorithms research, beginning with the results of Sleator and Tarjan showing that splay trees achieve static optimality for search trees, and that Move-toFront is constant competitive for the list update prob- lem [ST85a, ST85b]. This paper

Boosted Sampling: Approximation Algorithms forStochastic Optimization

by Anupam Gupta, Martin P R. Ravi, Amitabh Sinha
"... ABSTRACT Several combinatorial optimization problems choose elements tominimize the total cost of constructing a feasible solution that satisfies requirements of clients. In the STEINER TREE problem, forexample, edges must be chosen to connect terminals (clients); in VERTEX COVER, vertices must be c ..."
Abstract - Add to MetaCart
is costlier bya factor of?> 1. The goal is to minimize the first stage cost plusthe expected second stage cost. We give a general yet simple technique to adapt approximation al-gorithms for several deterministic problems to their stochastic versions via the following method. * First stage: Draw

Exact algorithms for the canadian traveller problem on paths and trees

by David Karger, Evdokia Nikolova , 2008
"... The Canadian Traveller problem is a stochastic shortest paths problem in which one learns the cost of an edge only when arriving at one of its endpoints. The goal is to find an adaptive policy (adjusting as one learns more edge lengths) that minimizes the expected cost of travel. The problem is know ..."
Abstract - Cited by 3 (1 self) - Add to MetaCart
The Canadian Traveller problem is a stochastic shortest paths problem in which one learns the cost of an edge only when arriving at one of its endpoints. The goal is to find an adaptive policy (adjusting as one learns more edge lengths) that minimizes the expected cost of travel. The problem

Energy-latency tradeoffs for data gathering in wireless sensor networks

by Yang Yu, Bhaskar Krishnamachari, Viktor K. Prasanna - In IEEE Infocom , 2004
"... Abstract — We study the problem of scheduling packet transmissions for data gathering in wireless sensor networks. The focus is to explore the energy-latency tradeoffs in wireless communication using techniques such as modulation scaling. The data aggregation tree – a multiple-source single-sink com ..."
Abstract - Cited by 116 (4 self) - Add to MetaCart
to the latency constraint. For the off-line problem, we propose (a) a numerical algorithm for the optimal solution, and (b) a pseudo-polynomial time approximation algorithm based on dynamic programming. We also discuss techniques for handling interference among the sensor nodes. Simulations have been conducted

Decision Trees for Function Evaluation Simultaneous Optimization of Worst and Expected Cost∗ Ferdinando Cicalese

by Eduardo Laber, Aline Medeiros Saettler , 2014
"... In several applications of automatic diagnosis and active learning a central problem is the evaluation of a discrete function by adaptively querying the values of its variables until the values read uniquely determine the value of the function. In general, the process of reading the value of a varia ..."
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or in expectation according to a prior distribution on the possible variables ’ assignments). Our algorithm builds a strategy (decision tree) which attains a logarithmic approxima-tion simultaneously for the expected and worst cost spent. This is best possible under the assumption that P 6 = NP. 1
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