Universal Traversal Sequences with Backtracking
نویسنده
چکیده
In this paper we introduce a new notion of traversal sequences that we call exploration sequences. Exploration sequences share many properties with the traversal sequences defined in [AKL+], but they also exhibit some new properties. In particular, they have an ability to backtrack, and their random properties are robust under choice of the probability distribution on labels. Further, we present extremely simple constructions of polynomial length universal exploration sequences for some previously studied classes of graphs (e.g., 2-regular graphs, cliques, expanders), and we also present universal exploration sequences for trees. Our constructions beat previously known lower-bounds on the length of universal traversal sequences.
منابع مشابه
Lower Bounds on Universal Traversal Sequences Based on Chains of Length Five
Universal traversal sequences for cycles require length (n 1:43), improving the previous bound of (n 1:33). For d 3, universal traversal sequences for d-regular graphs require length (d 0:57 n 2:43). For constant d, the best previous bound was (n 2:33).
متن کاملRandomized Backtracking in State Space Traversal
While exhaustive state space traversal is not feasible in reasonable time for complex concurrent programs, many techniques for efficient detection of concurrency errors and testing of concurrent programs have been introduced in recent years, such as directed search and context-bounded model checking. We propose to use depth-first traversal with randomized backtracking, where it is possible to b...
متن کاملConcepts for faster exploratory navigation
A navigation session across the web is a mix of forward linear traversals, cyclic paths and backtracks —which reflects the user’s exploratory navigation in finding relevant information for its particular interest. The user encounters two situations, both are about assessing the relevance of a linked document —before and after traversal —both involving some degree of cognitive overhead. This pap...
متن کاملA Cautionary Tale: False Efficiencies in the Traveling Salesman Problem*
The Traveling Salesman Problem provides an opportunity to explore whether attempts to optimize an algorithm in fact succeed or fail. Attempted optimizations themselves have time penalties in their execution and those time penalties may be greater than the improvements provided to the algorithm. When approaching the Traveling Salesman Problem not as a graph traversal problem but as a backtrackin...
متن کاملDefining Standard Prolog in Rewriting Logic
The coincidence between the model-theoretic and the procedural semantics of SLDresolution does not carry over to a Prolog system that also implements non-logical features like cut and whose depth-first search strategy is incomplete. The purpose of this paper is to present the key concepts of a new, simple operational semantics of Standard Prolog in the form of rewriting rules. We use a novel li...
متن کامل