Log-space Algorithms for Paths and Matchings in k-trees

Reachability and shortest path problems are NL-complete for general graphs. They are known to be in L for graphs of tree-width 2 [JT07]. However, for graphs of tree-width larger than 2, no bound better than NL is known. In this paper, we improve these bounds for k-trees, where k is a constant. In particular, the main results of our paper are log-space algorithms for reachability in directed k-trees, and for computation of shortest and longest paths in directed acyclic k-trees. Besides the path problems mentioned above, we also consider the problem of deciding whether a k-tree has a perfect macthing (decision version), and if so, finding a perfect match- ing (search version), and prove that these two problems are L-complete. These problems are known to be in P and in RNC for general graphs, and in SPL for planar bipartite graphs [DKR08]. Our results settle the complexity of these problems for the class of k-trees. The results are also applicable for bounded tree-width graphs, when a tree-decomposition is given as input. The technique central to our algorithms is a careful implementation of divide-and-conquer approach in log-space, along with some ideas from [JT07] and [LMR07].Comment: Accepted in STACS 201

All-Pairs Minimum Cuts in Near-Linear Time for Surface-Embedded Graphs

For an undirected $n$-vertex graph $G$ with non-negative edge-weights, we consider the following type of query: given two vertices $s$ and $t$ in $G$, what is the weight of a minimum $st$-cut in $G$? We solve this problem in preprocessing time $O(n\log^3 n)$ for graphs of bounded genus, giving the first sub-quadratic time algorithm for this class of graphs. Our result also improves by a logarithmic factor a previous algorithm by Borradaile, Sankowski and Wulff-Nilsen (FOCS 2010) that applied only to planar graphs. Our algorithm constructs a Gomory-Hu tree for the given graph, providing a data structure with space $O(n)$ that can answer minimum-cut queries in constant time. The dependence on the genus of the input graph in our preprocessing time is $2^{O(g^2)}$

Progressive Simplification of Polygonal Curves

Simplifying polygonal curves at different levels of detail is an important problem with many applications. Existing geometric optimization algorithms are only capable of minimizing the complexity of a simplified curve for a single level of detail. We present an $O(n^3m)$-time algorithm that takes a polygonal curve of n vertices and produces a set of consistent simplifications for m scales while minimizing the cumulative simplification complexity. This algorithm is compatible with distance measures such as the Hausdorff, the Fr\'echet and area-based distances, and enables simplification for continuous scaling in $O(n^5)$ time. To speed up this algorithm in practice, we present new techniques for constructing and representing so-called shortcut graphs. Experimental evaluation of these techniques on trajectory data reveals a significant improvement of using shortcut graphs for progressive and non-progressive curve simplification, both in terms of running time and memory usage.Comment: 20 pages, 20 figure

A comparative analysis of web-based GIS applications using usability metrics

With the rapid expansion of the internet, Web-based Geographic Information System (WGIS) applications have gained popularity, despite the interface of the WGIS application being difficult to learn and understand because special functions are needed to manipulate the maps. Hence, it is essential to evaluate the usability of WGIS applications. Usability is an important factor in ensuring the development of quality, usable software products. On the other hand, there are a number of standards and models in the literature, each of which describes usability in terms of various set of attributes. These models are vague and difficult to understand. Therefore, the primary purpose of this study is to compare five common usability models (Shackel, Nielsen, ISO 9241 P-11, ISO 9126-1 and QUIM) to identify usability metrics that have most frequently used in the previous models. The questionnaire method and the automated usability evaluation method by using Loop11 tool were used, in order to evaluate the usability metrics for three case studies of commonly used WGIS applications as Google maps, Yahoo maps, and MapQuest. Finally, those case studies were compared and analysed based on usability metrics that have been identified. Based on a comparative study, four usability metrics (Effectiveness, Efficiency, Satisfaction and Learnability) were identified. Those usability metrics were characterized by consistent, comprehensive, not vaguely and proper to evaluate the usability of WGIS applications. In addition, there was a positive correlation between these usability metrics. The comparative analysis indicates that Effectiveness, Satisfaction and Learnability were higher, and the Efficiency was lesser by using the Loop11 tool compared to questionnaire method for the three case studies. In addition, Yahoo Maps and MapQuest have usability metrics rate lesser than Google Maps by applying two methods. Therefore, Google Maps is more usable compared to Yahoo Maps and MapQuest

Labeling Schemes with Queries

We study the question of ``how robust are the known lower bounds of labeling schemes when one increases the number of consulted labels''. Let $f$ be a function on pairs of vertices. An $f$-labeling scheme for a family of graphs \cF labels the vertices of all graphs in \cF such that for every graph G\in\cF and every two vertices $u,v\in G$, the value $f(u,v)$ can be inferred by merely inspecting the labels of $u$ and $v$. This paper introduces a natural generalization: the notion of $f$-labeling schemes with queries, in which the value $f(u,v)$ can be inferred by inspecting not only the labels of $u$ and $v$ but possibly the labels of some additional vertices. We show that inspecting the label of a single additional vertex (one {\em query}) enables us to reduce the label size of many labeling schemes significantly