Dijkstra's single-source shortest-path algorithm (DA) is one of the well-known, fundamental algorithms in computer science and related fields. DA is commonly taught in undergraduate courses. Uniform-cost search (UCS) is a simple version of the best-first search scheme which is logically equivalent to DA. In this paper I compare the two algorithms and show their similarities and differences. I claim that UCS is superior to DA in almost all aspects. It is easier to understand and implement. Its time and memory needs are also smaller. The reason that DA is taught in universities and classes around the world is probably only historical. I encourage people to stop using and teaching DA, and focus on UCS only.

In many applications of heuristic search, insufficient time isavailable to find provably optimal solutions. We consider thecontract search problem: finding the best solution possible within agiven time limit. The conventional approach to this problem is to usean interruptible anytime algorithm. Such algorithms return a sequenceof improving solutions until interuppted and do not consider theapproaching deadline during the course of the search. We propose anew approach, Deadline Aware Search, that explicitly takes the deadlineinto account and attempts to use all available time to find a singlehigh-quality solution. This algorithm is simple and fully general: itmodifies best-first search with on-line pruning. Empirical results onvariants of gridworld navigation, the sliding tile puzzle, and dynamicrobot navigation show that our method can surpass the leading anytimealgorithms across a wide variety of deadlines.

Move pruning is a low-overhead technique for reducing the size of a depth first search tree. The existing algorithm for automatically discovering move pruning information is restricted to games where all moves can be applied to every state. This paper demonstrates an algorithm which handles a general class of single player games. It gives experimental results for our technique, demonstrating both the applicability to a range of games, and the reduction in search tree size. We also provide some conditions under which move pruning is safe, and when it may interfere with other search reduction techniques.

In the Canadian Traveler Problem (CTP) a traveling agent is given a weighted graph, where some of the edges may be blocked, with a known probability. The agent needs to travel to a given goal. A solution for CTP is a policy, that has the smallest expected traversal cost. CTP is intractable. Previous work has focused on the case of a single agent. We generalize CTP to a repeated task version where a number of agents need to travel to the same goal, minimizing their combined travel cost. We provide optimal algorithms for the special case of disjoint path graphs. Based on a previous UCT-based approach for the single agent case, a framework is developed for the multi-agent case and four variants are given - two of which are based on the results for disjoint-path graphs. Empirical results show the benefits of the suggested framework and the resulting heuristics. For small graphs where we could compare to optimal policies, our approach achieves near optimal results at only a fraction of the computation cost.

Social networks play an increasingly important role in today's society. Special characteristics of these networks make them challenging domains for the search community. In particular, social networks of users can be viewed as search graphs of nodes, where the cost of obtaining information about a node can be very high. This paper addresses the search problem of identifying the degree of separation between two users. New search techniques are introduced to provide optimal or near-optimal solutions. The experiments are performed using Twitter, and they show an improvement of several orders of magnitude over greedy approaches. Our optimal algorithm finds an average degree of separation of 3.43 between two random Twitter users, requiring an average of only 67 requests for information over the Internet to Twitter. A near-optimal solution of length 3.88 can be found by making an average of 13.3 requests.

Complexity analysis of planning is problematic. Even very simple planning languages are PSPACE-complete, yet cannot model many simple problems naturally. Many languages with much more powerful features are also PSPACE-complete. It is thus difficult to separate planning languages in a useful way and to get complexity figures that better reflect reality. This paper introduces new methods for complexity analysis of planning and similar combinatorial search problems, in order to achieve more precision and complexity separations than standard methods allow. Padding instances with the solution size yields a complexity measure that is immune to this factor and reveals other causes of hardness, that are otherwise hidden. Further combining this method with limited non-determinism improves the precision, making even finer separations possible. We demonstrate with examples how these methods can narrow the gap between theory and practice.

Rapidly-exploring random trees (RRTs) are data structures and search algorithms designed to be used in continuous path planning problems. They are one of the most successful state-of-the-art techniques as they offer a great degree of flexibility and reliability. However, their use in other search domains has not been thoroughly analyzed. In this work we propose the use of RRTs as a search algorithm for automated planning. We analyze the advantages that this approach has over previously used search algorithms and the challenges of adapting RRTs for implicit and discrete search spaces.

Sparse coding consists in representing signals as sparse linear combinations of atoms selected from a dictionary. We consider an extension of this framework where the atoms are further assumed to be embedded in a tree. This is achieved using a recently introduced tree-structured sparse regularization norm, which has proven useful in several applications. This norm leads to regularized problems that are difficult to optimize, and we propose in this paper efficient algorithms for solving them. More precisely, we show that the proximal operator associated with this norm is computable exactly via a dual approach that can be viewed as the composition of elementary proximal operators. Our procedure has a complexity linear, or close to linear, in the number of atoms, and allows the use of accelerated gradient techniques to solve the tree-structured sparse approximation problem at the same computational cost as traditional ones using the L1-norm. Our method is efficient and scales gracefully to millions of variables, which we illustrate in two types of applications: first, we consider fixed hierarchical dictionaries of wavelets to denoise natural images. Then, we apply our optimization tools in the context of dictionary learning, where learned dictionary elements naturally organize in a prespecified arborescent structure, leading to a better performance in reconstruction of natural image patches. When applied to text documents, our method learns hierarchies of topics, thus providing a competitive alternative to probabilistic topic models.

This paper presents a Bayesian approach to symbol and phase inference in a phase-unsynchronized digital receiver. It primarily extends [Quinn 2011] to the multi-symbol case, using the variational Bayes (VB) approximation to deal with the combinatorial complexity of the phase inference in this case. The work provides a fully Bayesian extension of the EM-based framework underlying current turbo-synchronization methods, since it induces a von Mises prior on the time-invariant phase parmeter. As a result, we achieve tractable iterative algorithms with improved robustness in low SNR regimes, compared to the current EM-based approaches. As a corollary to our analysis we also discover the importance of prior regularization in elegantly tackling the significant problem of phase ambiguity.

Induction is the process by which we obtain predictive laws or theories or models of the world. We consider the structural aspect of induction. We answer the question as to whether we can find a finite and minmalistic set of operations on structural elements in terms of which any theory can be expressed. We identify abstraction (grouping similar entities) and super-structuring (combining topologically e.g., spatio-temporally close entities) as the essential structural operations in the induction process. We show that only two more structural operations, namely, reverse abstraction and reverse super-structuring (the duals of abstraction and super-structuring respectively) suffice in order to exploit the full power of Turing-equivalent generative grammars in induction. We explore the implications of this theorem with respect to the nature of hidden variables, radical positivism and the 2-century old claim of David Hume about the principles of connexion among ideas.