Gerhard Trippen

Exploring an unknown graph efficiently

We study the problem of exploring an unknown, strongly connected directed graph. Starting at some node of the graph, we must visit every edge and every node at least once. The goal is to minimize the number of edge traversals. It is known that the competitive ratio of online algorithms for this problem depends on the deficiency d of the graph, which is the minimum number of edges that must be added to make the graph Eulerian. We present the first deterministic online exploration algorithm whose competitive ratio is polynomial in d (it is O(d8)).

Competitive Online Approximation of the Optimal Search Ratio

How efficiently can we search an unknown environment for a goal in unknown position? How much would it help if the environment were known? We answer these questions for simple polygons and for general graphs, by providing online search strategies that are as good as the best offline search algorithms, up to a constant factor. For other settings we prove that no such online algorithms exist.

Experimental studies of graph traversal algorithms

We conduct an experimental evaluation of all major online graph traversal algorithms. This includes many simple natural algorithms as well as more sophisticated strategies. The observations we made watching the animated algorithms explore the graphs in the interactive experiments motivated us to introduce some variants of the original algorithms. Since the theoretical bounds for deterministic online algorithms are rather bad and no better bounds for randomized algorithms are known, our work helps to provide a better insight into the practical performance of these algorithms on various graph families. It is to observe that all the tested algorithm have a performance very close to the optimum offline algorithm in a huge family of random graphs. Only few very specific lower bound examples cause bad results.

Plans, patterns, and move categories guiding a highly selective search

In this paper we present our ideas for an Arimaa-playing program (also called a bot) that uses plans and pattern matching to guide a highly selective search. We restrict move generation to moves in certain move categories to reduce the number of moves considered by the bot significantly. Arimaa is a modern board game that can be played with a standard Chess set. However, the rules of the game are not at all like those of Chess. Furthermore, Arimaa was designed to be as simple and intuitive as possible for humans, yet challenging for computers. While all established Arimaa bots use alpha-beta search with a variety of pruning techniques and other heuristics ending in an extensive positional leaf node evaluation, our new bot, Rat, starts with a positional evaluation of the current position. Based on features found in the current position – supported by pattern matching using a directed position graph – our bot Rat decides which of a given set of plans to follow. The plan then dictates what types of moves can be chosen. This is another major difference from bots that generate “all” possible moves for a particular position. Rat is only allowed to generate moves that belong to certain categories. Leaf nodes are evaluated only by a straightforward material evaluation to help avoid moves that lose material. This highly selective search looks, on average, at only 5 moves out of 5,000 to over 40,000 possible moves in a middle game position.

On the effectiveness of visualizations in a theory of computing course

We report on two tests we performed in Hong Kong and Shanghai to verify the hypothesis that one can learn better when being given access to visualizations beyond the standard verbal explanations in a classroom. The outcome of the first test at HKUST was inconclusive, while the second test at Fudan University showed a clear advantage for those students who had access to visualizations.

Algorithms and Computation

Puzzles, Art, and Magic with Algorithms.- The ABCs of AVDs: Geometric Retrieval Made Simple.- Pareto Optimality in House Allocation Problems.- Property-Preserving Data Reconstruction.- On the Monotone Circuit Complexity of Quadratic Boolean Functions.- Generalized Function Matching.- Approximate Distance Oracles for Graphs with Dense Clusters.- Multicriteria Global Minimum Cuts.- Polyline Fitting of Planar Points Under Min-sum Criteria.- A Generalization of Magic Squares with Applications to Digital Halftoning.- Voronoi Diagrams with a Transportation Network on the Euclidean Plane.- Structural Alignment of Two RNA Sequences with Lagrangian Relaxation.- Poly-APX- and PTAS-Completeness in Standard and Differential Approximation.- Efficient Algorithms for k Maximum Sums.- Equipartitions of Measures by 2-Fans.- Augmenting the Edge-Connectivity of a Spider Tree.- On Nash Equilibria for Multicast Transmissions in Ad-Hoc Wireless Networks.- Structural Similarity in Graphs.- Flexibility of Steiner Trees in Uniform Orientation Metrics.- Random Access to Advice Strings and Collapsing Results.- Bounding the Payment of Approximate Truthful Mechanisms.- The Polymatroid Steiner Problems.- Geometric Optimization Problems Over Sliding Windows.- On-Line Windows Scheduling of Temporary Items.- Generalized Geometric Approaches for Leaf Sequencing Problems in Radiation Therapy.- An Efficient Exact Algorithm for the Minimum Ultrametric Tree Problem.- On the Range Maximum-Sum Segment Query Problem.- An Efficient Algorithm for Finding Maximum Cycle Packings in Reducible Flow Graphs.- Efficient Job Scheduling Algorithms with Multi-type Contentions.- Superimposing Voronoi Complexes for Shape Deformation.- On Partial Lifting and the Elliptic Curve Discrete Logarithm Problem.- Guarding Art Galleries by Guarding Witnesses.- On p-Norm Based Locality Measures of Space-Filling Curves.- Composability of Infinite-State Activity Automata.- Error Compensation in Leaf Root Problems.- On Compact and Efficient Routing in Certain Graph Classes.- Randomized Insertion and Deletion in Point Quad Trees.- Diagnosis in the Presence of Intermittent Faults.- Three-Round Adaptive Diagnosis in Binary n-Cubes.- Fast Algorithms for Comparison of Similar Unordered Trees.- GCD of Random Linear Forms.- On the Hardness and Easiness of Random 4-SAT Formulas.- Minimum Common String Partition Problem: Hardness and Approximations.- On the Complexity of Network Synchronization.- Counting Spanning Trees and Other Structures in Non-constant-jump Circulant Graphs.- Adaptive Spatial Partitioning for Multidimensional Data Streams.- Paired Pointset Traversal.- Approximated Two Choices in Randomized Load Balancing.- Space-Efficient and Fast Algorithms for Multidimensional Dominance Reporting and Counting.- Local Gapped Subforest Alignment and Its Application in Finding RNA Structural Motifs.- The Maximum Agreement of Two Nested Phylogenetic Networks.- Sequences of Radius k: How to Fetch Many Huge Objects into Small Memory for Pairwise Computations.- New Bounds on Map Labeling with Circular Labels.- Optimal Buffer Management via Resource Augmentation.- Oriented Paths in Mixed Graphs.- Polynomial Deterministic Rendezvous in Arbitrary Graphs.- Distributions of Points and Large Quadrangles.- Cutting Out Polygons with Lines and Rays.- Advantages of Backward Searching - Efficient Secondary Memory and Distributed Implementation of Compressed Suffix Arrays.- Inner Rectangular Drawings of Plane Graphs.- Approximating the Minmax Subtree Cover Problem in a Cactus.- Boundary-Optimal Triangulation Flooding.- Exact Computation of Polynomial Zeros Expressible by Square Roots.- Many-to-Many Disjoint Path Covers in a Graph with Faulty Elements.- An O(nlog n)-Time Algorithm for the Maximum Constrained Agreement Subtree Problem for Binary Trees.- Planning the Transportation of Multiple Commodities in Bidirectional Pipeline Networks.- Efficient Algorithms for the Hotlink Assignment Problem: The Worst Case Search.- Dynamic Tree Cross Products.- Spanners, Weak Spanners, and Power Spanners for Wireless Networks.- Techniques for Indexing and Querying Temporal Observations for a Collection of Objects.- Approximation Algorithms for the Consecutive Ones Submatrix Problem on Sparse Matrices.- The Two-Guard Problem Revisited and Its Generalization.- Canonical Data Structure for Interval Probe Graphs.- Efficient Algorithms for the Longest Path Problem.- Randomized Algorithms for Motif Detection.- Weighted Coloring on Planar, Bipartite and Split Graphs: Complexity and Improved Approximation.- Sweeping Graphs with Large Clique Number.- A Slightly Improved Sub-cubic Algorithm for the All Pairs Shortest Paths Problem with Real Edge Lengths.