The rigorous theoretical analyses of algorithms for #SAT have been proposed in the literature. As we know, previous algorithms for solving #SAT have been analyzed only regarding the number of variables as the parameter. However, the time complexity for solving #SAT instances depends not only on the number of variables, but also on the number of clauses. Therefore, it is significant to exploit the time complexity from the other point of view, i.e. the number of clauses. In this paper, we present algorithms for solving #2-SAT and #3-SAT with rigorous complexity analyses using the number of clauses as the parameter. By analyzing the algorithms, we obtain the new worst-case upper bounds O(1.1892m) for #2-SAT and O(1.4142m) for #3-SAT, where m is the number of clauses.

The feasible solutions of the traveling salesman problem with pickup and delivery (TSPPD) are represented by vertex lists in existing literature. However, when the TSPPD requires that the loading and unloading operations must be performed in a last-in-first-out (LIFO) manner, we show that its feasible solutions can be represented by trees. Consequently, we develop a variable neighbourhood search (VNS) heuristic for the TSPPD with last-in-first-out loading (TSPPDL) involving several search operators based on the tree data structure. Experiments show that our VNS heuristic is superior to the current best heuristics for TSPPDL in terms of both solution quality and computing time.

On the surface, bidirectional search (BDS) is an attractive idea with the potential for significant asymptotic reductions in search effort. However, the results in practice often fall far short of expectations. We introduce a new bidirectional search algorithm, Single-Frontier Bidirectional Searc (SFBDS). Unlike traditional BDS which keeps two frontiers, SFBDS uses a single frontier. Each node in the tree can be seen as an independent task of finding the shortest path between the current start and current goal. At a particular node we can decide to search from start to goal or from goal to start, choosing the direction with the highest potential for minimizing the total work done. Theoretical results give insights as to when this approach will work and experimental data validates the algorithm for a broad range of domains.

We consider planning domains with both discrete and continuous changes. Continuous change occurs especially when agents share time-dependent critical resources. In these cases, besides discrete and continuous changes, their interactions should also be taken into consideration. However concurrency of durative actions with interacting continuous effects cannot be exploited by existing temporal planners. To overcome this problem, we propose an action lifting approach and we analyze path sharing problem to illustrate interaction of continuous linear effects in the planning domain.

Data sparsity is a major problem for collaborative filtering (CF) techniques in recommender systems, especially for new users and items. We observe that, while our target data are sparse for CF systems, related and relatively dense auxiliary data may already exist in some other more mature application domains. In this paper, we address the data sparsity problem in a target domain by transferring knowledge about both users and items from auxiliary data sources. We observe that in different domains the user feedbacks are often heterogeneous such as ratings vs. clicks. Our solution is to integrate both user and item knowledge in auxiliary data sources through a principled matrix-based transfer learning framework that takes into account the data heterogeneity. In particular, we discover the principle coordinates of both users and items in the auxiliary data matrices, and transfer them to the target domain in order to reduce the effect of data sparsity. We describe our method, which is known as coordinate system transfer or CST, and demonstrate its effectiveness in alleviating the data sparsity problem in collaborative filtering. We show that our proposed method can significantly outperform several state-of-the-art solutions for this problem.

It is well known that there cannot be a single "best" heuristic for optimal planning in general. One way of overcoming this is by combining admissible heuristics (e.g. by using their maximum), which requires computing numerous heuristic estimates at each state. However, there is a tradeoff between the time spent on computing these heuristic estimates for each state, and the time saved by reducing the number of expanded states. We present a novel method that reduces the cost of combining admissible heuristics for optimal search, while maintaining its benefits. Based on an idealized search space model, we formulate a decision rule for choosing the best heuristic to compute at each state. We then present an active online learning approach for that decision rule, and employ the learned model to decide which heuristic to compute at each state. We evaluate this technique empirically, and show that it substantially outperforms each of the individual heuristics that were used, as well as their regular maximum.

A number of algorithms have been proposed for the Minimum Vertex Cover problem. However, they are far from satisfactory, especially on hard instances. In this paper, we introduce Edge Weighting Local Search (EWLS), a new local search algorithm for the Minimum Vertex Cover problem. EWLS is based on the idea of extending a partial vertex cover into a vertex cover. A key point of EWLS is to find a vertex set that provides a tight upper bound on the size of the minimum vertex cover. To this purpose, EWLS employs an iterated local search procedure, using an edge weighting scheme which updates edge weights when stuck in local optima. Moreover, some sophisticated search strategies have been taken to improve the quality of local optima. Experimental results on the broadly used DIMACS benchmark show that EWLS is competitive with the current best heuristic algorithms, and outperforms them on hard instances. Furthermore, on a suite of difficult benchmarks, EWLS delivers the best results and sets a new record on the largest instance.

Multiple Kernel Learning (MKL) can be formulated as a convex-concave minmax optimization problem, whose saddle point corresponds to the optimal solution to MKL. Most MKL methods employ the L1-norm simplex constraints on the combination weights of kernels, which therefore involves optimization of a non-smooth function of the kernel weights. These methods usually divide the optimization into two cycles: one cycle deals with the optimization on the kernel combination weights, and the other cycle updates the parameters of SVM. Despite the success of their efficiency, they tend to discard informative complementary kernels. To improve accuracy, we introduce smoothness to the optimization procedure. Furthermore, we transform the optimization into a single smooth convex optimization problem and employ the Nesterov’s method to efficiently solve the optimization problem. Experiments on benchmark data sets demonstrate that the proposed algorithm clearly improves current MKL methods in a number scenarios.

Much of the ongoing explosion of digital content is in the form of text. This content is a virtual gold-mine of information that can inform a range of social, governmental, and business decisions. For example, using content available on blogs and social networking sites businesses can find out what its customers are saying about their products and services. In the digital age where customer is king, the business value of ascertaining consumer sentiment cannot be overstated. People express sentiments in myriad ways. At times, they use simple, direct assertions, but most often they use sentences involving comparisons, conjunctions expressing multiple and possibly opposing sentiments about multiple features and entities,and pronominal references whose resolution requires discourse level context. Frequently people use abbreviations, slang, SMSese, idioms and metaphors. Understanding the latter also requires common sense reasoning. In this paper, we present iSEE, a fully implemented sentiment extraction engine, which makes use of statistical methods, classical NLU techniques, common sense reasoning, and probabilistic inference to extract entity and feature specific sentiment from complex sentences and dialog. Most of the components of iSEE are domain independent and the system can be generalized to new domains by simply adding domain relevant lexicons.

This paper presents a machine learning approach for accurate estimation of energy expenditure using a fusion of accelerometer and heart rate sensing. To address short comings in existing off-the-shelf solutions, we designed Jog Falls, an end to end system for weight management in collaboration with physicians in India. This system is meant to enable people to accurately monitor their energy expenditure and intake and make educated tradeoffs to reach their weight goals. In this paper we describe the sensing components of Jog Falls and focus on the energy expenditure estimation algorithm. We present results from controlled experiments in the lab, as well results from a 15 participant user study over a period of 63 days. We show how our algorithm mitigates many of the issues in existing solutions and yields more accurate results.