Maximum Persistency in Energy Minimization

We consider discrete pairwise energy minimization problem (weighted constraint satisfaction, max-sum labeling) and methods that identify a globally optimal partial assignment of variables. When finding a complete optimal assignment is intractable, determining optimal values for a part of variables is an interesting possibility. Existing methods are based on different sufficient conditions. We propose a new sufficient condition for partial optimality which is: (1) verifiable in polynomial time (2) invariant to reparametrization of the problem and permutation of labels and (3) includes many existing sufficient conditions as special cases. We pose the problem of finding the maximum optimal partial assignment identifiable by the new sufficient condition. A polynomial method is proposed which is guaranteed to assign same or larger part of variables than several existing approaches. The core of the method is a specially constructed linear program that identifies persistent assignments in an arbitrary multi-label setting.Comment: Extended technical report for the CVPR 2014 paper. Update: correction to the proof of characterization theore

Restricted Value Iteration: Theory and Algorithms

Value iteration is a popular algorithm for finding near optimal policies for POMDPs. It is inefficient due to the need to account for the entire belief space, which necessitates the solution of large numbers of linear programs. In this paper, we study value iteration restricted to belief subsets. We show that, together with properly chosen belief subsets, restricted value iteration yields near-optimal policies and we give a condition for determining whether a given belief subset would bring about savings in space and time. We also apply restricted value iteration to two interesting classes of POMDPs, namely informative POMDPs and near-discernible POMDPs

The Nature of Retrograde Analysis for Chinese Chess

Retrograde analysis has been successfully applied to solve Awari and construct 6-piece Western chess endgame databases. However, its application to Chinese chess is limited because of the special rules about indefinite move sequences. Problems caused by the most influential rule, checking indefinitely were successfully solved in practical cases, with $50$ selected endgame databases constructed in accord with this rule, where the 60-move-rule was ignored. Other special rules have much less impact on contaminating the databases, as verified by the rule-tolerant algorithms. For constructing complete endgame databases, we need rigorous algorithms. There are two rule sets in Chinese chess: Asian rule set and Chinese rule set. In this paper, an algorithm is successfully developed to construct endgame databases in accord with the Asian rule set. The graph-theoretical properties are also explored as well

Adding Logical Operators to Tree Pattern Queries on Graph-Structured Data

As data are increasingly modeled as graphs for expressing complex relationships, the tree pattern query on graph-structured data becomes an important type of queries in real-world applications. Most practical query languages, such as XQuery and SPARQL, support logical expressions using logical-AND/OR/NOT operators to define structural constraints of tree patterns. In this paper, (1) we propose generalized tree pattern queries (GTPQs) over graph-structured data, which fully support propositional logic of structural constraints. (2) We make a thorough study of fundamental problems including satisfiability, containment and minimization, and analyze the computational complexity and the decision procedures of these problems. (3) We propose a compact graph representation of intermediate results and a pruning approach to reduce the size of intermediate results and the number of join operations -- two factors that often impair the efficiency of traditional algorithms for evaluating tree pattern queries. (4) We present an efficient algorithm for evaluating GTPQs using 3-hop as the underlying reachability index. (5) Experiments on both real-life and synthetic data sets demonstrate the effectiveness and efficiency of our algorithm, from several times to orders of magnitude faster than state-of-the-art algorithms in terms of evaluation time, even for traditional tree pattern queries with only conjunctive operations.Comment: 16 page

A Tight Lower Bound for Decrease-Key in the Pure Heap Model

We improve the lower bound on the amortized cost of the decrease-key operation in the pure heap model and show that any pure-heap-model heap (that has a \bigoh{\log n} amortized-time extract-min operation) must spend \bigom{\log\log n} amortized time on the decrease-key operation. Our result shows that sort heaps as well as pure-heap variants of numerous other heaps have asymptotically optimal decrease-key operations in the pure heap model. In addition, our improved lower bound matches the lower bound of Fredman [J. ACM 46(4):473-501 (1999)] for pairing heaps [M.L. Fredman, R. Sedgewick, D.D. Sleator, and R.E. Tarjan. Algorithmica 1(1):111-129 (1986)] and surpasses it for pure-heap variants of numerous other heaps with augmented data such as pointer rank-pairing heaps.Comment: arXiv admin note: substantial text overlap with arXiv:1302.664

JPS Algorithm Adaptation and Optimization to Three-dimensional Space

The aim of this thesis is to research the principles of the Jump Point Search (JPS) pathfinding algorithm and study the possibilities of adapting JPS to three-dimensional environment. JPS is partly based on A* algorithm but its performance is significantly better than the original A* algorithm. At the moment, there is no known 3D pathfinding algorithm published which uses the same principles as JPS. The motivation of this work is to find out what changes will be needed on the algorithm so that it will work in 3D and improve performance of the 3D version. Special target is performance comparison to the original A* algorithm and 3D JPS algorithm on inside a layered 3D space (building). Pathfinding inside building is common pathfinding problem in a video games as well it has importance also in real life. The algorithms were implemented by using Unity 3D game engine with C# language. For the purpose of research, A* and JPS algorithms were tested in the same 3D test environment. This arrangement made it possible to run the algorithms with the same test data to get a meaningful performance comparison between the algorithms. As a result, this gives also the exact principles how to adapt JPS Algorithm on a 3D environment. Moreover, it provides a novel idea and practical implementation on how to optimize the JPS 3D algorithm to get an improved performance. The presented results also include performance measurements for comparing JPS 3D method and its optimized variant in different environments

Optimizing I/O for Big Array Analytics

Big array analytics is becoming indispensable in answering important scientific and business questions. Most analysis tasks consist of multiple steps, each making one or multiple passes over the arrays to be analyzed and generating intermediate results. In the big data setting, I/O optimization is a key to efficient analytics. In this paper, we develop a framework and techniques for capturing a broad range of analysis tasks expressible in nested-loop forms, representing them in a declarative way, and optimizing their I/O by identifying sharing opportunities. Experiment results show that our optimizer is capable of finding execution plans that exploit nontrivial I/O sharing opportunities with significant savings.Comment: VLDB201