We consider the problem of maintaining a large matching or a small vertex cover in a dynamically changing graph. Each update to the graph is either an edge deletion or an edge insertion. We give the first data structure that simultaneously achieves a constant approximation factor and handles a sequence of k updates in k · polylog(n) time. Previous data structures require a polynomial amount of ...

Approximate dynamic programming (ADP) has emerged as a powerful tool for tackling a diverse collection of stochastic optimization problems. Reflecting the wide diversity of problems, ADP (including research under names such as reinforcement learning, adaptive dynamic programming and neuro-dynamic programming) has become an umbrella for a wide range of algorithmic strategies. Most of these invol...

Unmanned Aircraft Systems (UAS) have the potential to perform many of the dangerous missions currently flown by manned aircraft. Yet, the complexity of some tasks, such as air combat, have precluded UAS from successfully carrying out these missions autonomously. This paper presents a formulation of the one-on-one air combat maneuvering problem and an approximate dynamic programming approach to ...

We consider the use of quadratic approximate value functions for stochastic control problems with inputaffine dynamics and convex stage cost and constraints. Evaluating the approximate dynamic programming policy in such cases requires the solution of an explicit convex optimization problem, such as a quadratic program, which can be carried out efficiently. We describe a simple and general metho...

Approximate dynamic programming (ADP) is a general methodological framework for multistage stochastic optimization problems in transportation, finance, energy, and other applications where scarce resources must be allocated optimally. We propose a new approach to the exploration/exploitation dilemma in ADP. First, we show how a Bayesian belief structure can be used to express uncertainty about ...

We propose and examine a method of approximate dynamic programming for Markov decision processes based on structured problem representations. We assume an MDP is represented using a dynamic Bayesian network, and construct value functions using decision trees as our function representation. The size of the representation is kept within acceptable limits by pruning these value trees so that leave...

h this paper we address the issue of kinodynamic motion planning. Given a point that moves with bounded acceleration and velocity, we wish to find the time-optimal trajectory from a start state to a goal state (a state consists of both a position and a velocity). As finding exact optimal solutions to this problem seems very hard, we present a provably good approximation algorithm using the L2 n...

We present an approximate dynamic programming approach for making ambulance redeployment decisions in an emergency medical service system. The primary decision is where we should redeploy idle ambulances so as to maximize the number of calls reached within a given delay threshold. We begin by formulating this problem as a dynamic program. To deal with the high-dimensional and uncountable state ...

We consider dynamic and online variants of 2D pattern matching between an m×m pattern and an n× n text. All the algorithms we give are randomised and give correct outputs with at least constant probability. – For dynamic 2D exact matching where updates change individual symbols in the text, we show updates can be performed in O(log n) time and queries in O(log m) time. – We then consider a mode...