Local Search is one of the fundamental approaches to combinatorial optimization and it is used throughout AI. Several local search algorithms are based on searching the k -exchange neighborhood. This is the set of solutions that can be obtained from the current solution by exchanging at most k elements. As a rule of thumb, the larger k is, the better are the chances of finding an improved solution. However, for inputs of size n, a naive brute-force search of the k-exchange neighborhood requires n (O( k )) time, which is not practical even for very small values of k. Fellows et al. (IJCAI 2009) studied whether this brute-force search is avoidable and gave positive and negative answers for several combinatorial problems. They used the notion of local search in a strict sense. That is, an improved solution needs to be found in the k-exchange neighborhood even if a global optimum can be found efficiently. In this paper we consider a natural relaxation of local search, called permissive local search (Marx and Schlotter, IWPEC 2009) and investigate whether it enhances the domain of tractable inputs. We exemplify this approach on a fundamental combinatorial problem, Vertex Cover. More precisely, we show that for a class of inputs, finding an optimum is hard, strict local search is hard, but permissive local search is tractable. We carry out this investigation in the framework of parameterized complexity.

The increasing availability of “utility computing” resources such as clouds, grids, and massively parallel shared clusters can provide practically unlimited processing and memory capacity on demand, at some cost per unit of resource usage. This requires a new perspective in the design and evaluation of parallel search algorithms. Previous work in parallel search implicitly assumed ownership of a cluster with a static amount of CPU cores and RAM, and emphasized wallclock runtime. With utility computing resources, trade-offs between performance and monetary costs must be considered. This paper considers dynamically increasing the usage of utility computing resources until a problem is solved. Efficient resource allocation policies are analyzed in comparison with an optimal allocation strategy. We evaluate our iterative allocation strategy by applying it to the HDA* parallel search algorithm. The experimental results validate our theoretical predictions. They show that, in practice, the costs incurred by iterative allocation are reasonably close to an optimal (but a priori unknown) policy, and are significantly better than the worst-case analytical bounds.

In this paper, we propose two new strategies to design efficient local search algorithms for the minimum vertex cover (MVC) problem. There are two main drawbacks in state-of-the-art MVC local search algorithms: First, they select a pair of vertices to be exchanged simultaneously, which is time consuming; Second, although they use edge weighting techniques, they do not have a strategy to decrease the weights. To address these drawbacks, we propose two new strategies: two stage exchange and edge weighting with forgetting. The two stage exchange strategy selects two vertices to be exchanged separately and performs the exchange in two stages. The strategy of edge weighting with forgetting not only increases weights of uncovered edges, but also decreases some weights for each edge periodically. We utilize these two strategies to design a new algorithm dubbed NuMVC. The experimental results show that NuMVC significantly outperforms existing state-of-the-art heuristic algorithms on most of the hard DIMACS instances and all instances in the hard random BHOSLIB benchmark.

The paper focuses on finding the m best solutions to combinatorial optimization problems using Best-First or Branchand- Bound search. Specifically, we present m-A*, extending the well-known A* to the m-best task, and prove that all its desirable properties, including soundness, completeness and optimal efficiency, are maintained. Since Best-First algorithms have memory problems, we also extend the memoryefficient Depth-First Branch-and-Bound to the m-best task. We extend both algorithms to optimization tasks over graphical models (e.g., Weighted CSP and MPE in Bayesian networks), provide complexity analysis and an empirical evaluation. Our experiments with 5 variants of Best-First and Branch-and-Bound confirm that Best-First is largely superior when memory is available, but Branch-and-Bound is more robust, while both styles of search benefit greatly when the heuristic evaluation function has increased accuracy.

Alpha-Beta pruning is one of the most powerful and fundamental MiniMax search improvements. It was designed for sequential two-player zero-sum perfect information games. In this paper we introduce an Alpha-Beta-like sound pruning method for the more general class of “stacked matrix games” that allow for simultaneous moves by both players. This is accomplished by maintaining upper and lower bounds for achievable payoffs in states with simultaneous actions and dominated action pruning based on the feasibility of certain linear programs. Empirical data shows considerable savings in terms of expanded nodes compared to naive depth-first move computation without pruning.

The current state-of-the-art algorithm for optimal coalition structure generation is IDP-IP — an algorithm that combines IDP (a dynamic programming algorithm due to Rahwan and Jennings, AAAI'08) with IP (a tree-search algorithm due to Rahwan et al., JAIR'09). In this paper we analyse IDP-IP, highlight its limitations, and then develop a new approach for combining IDP with IP that overcomes these limitations.

It has been shown recently that the complexity of belief tracking in deterministic conformant and contingent planning is exponential in a width parameter that is often bounded and small. In this work, we introduce a new width notion that applies to non-deterministic conformant and contingent problems as well. We also develop a belief tracking algorithm for non-deterministic problems that is exponential in the problem width, analyze the width of non-deterministic benchmarks, compare the new notion to the previous one over deterministic problems, and present experimental results.

This paper is devoted to sequential decision making with Rank Dependent expected Utility (RDU). This decision criterion generalizes Expected Utility and enables to model a wider range of observed (rational) behaviors. In such a sequential decision setting, two conflicting objectives can be identified in the assessment of a strategy: maximizing the performance viewed from the initial state (optimality), and minimizing the incentive to deviate during implementation (deviation-proofness). In this paper, we propose a minimax regret approach taking these two aspects into account, and we provide a search procedure to determine an optimal strategy for this model. Numerical results are presented to show the interest of the proposed approach in terms of optimality, deviation-proofness and computability.

Robotic exploration is an on-line problem in which autonomous mobile robots incrementally discover and map the physical structure of initially unknown environments. Usually, the performance of exploration strategies used to decide where to go next is not compared against the optimal performance obtainable in the test environments, because the latter is generally unknown. In this paper, we present a method to calculate an approximation of the optimal (shortest) exploration path in an arbitrary environment. We consider a mobile robot with limited visibility, discretize a two-dimensional environment with a regular grid, and formulate a search problem for finding the optimal exploration path in the grid, which is solved using A*. Experimental results show the viability of our approach for realistically large environments and its potential for better assessing the performance of on-line exploration strategies.

High dimensional nearest neighbor search is a fundamental problem and has found applications in many domains. Although many hashing based approaches have been proposed for approximate nearest neighbor search in high dimensional space, one main drawback is that they often return many false positives that need to be filtered out by a post procedure. We propose a novel method to address this limitation in this paper. The key idea is to introduce a filtering procedure within the search algorithm, based on the compressed sensing theory, that effectively removes the false positive answers. We first obtain a sparse representation for each data point by the landmark based approach, after which we solve the nearly duplicate search that the difference between the query and its nearest neighbors forms a sparse vector living in a small ℓp ball, where p ≤ 1. Our empirical study on real-world datasets demonstrates the effectiveness of the proposed approach compared to the state-of-the-art hashing methods.