Kazunori Mizuno

Constructive generation of very hard 3-colorability instances

Graph colorability (COL), is a typical constraint satisfaction problem to which phase transition phenomena (PTs), are important in the computational complexity of combinatorial search algorithms. PTs are significant and subtle because, in the PT region, extraordinarily hard problem instances are found, which may require exponential-order computational time to solve. To clarify PT mechanism, many studies have been undertaken to produce very hard instances, many of which were based on generate-and-test approaches. We propose a rather systematic or constructive algorithm that repeats the embedding of 4-critical graphs to arbitrarily generate large extraordinarily hard 3-colorability instances. We demonstrated experimentally that the computational cost to solve our generated instances is of an exponential order of the number of vertices by using a few actual coloring algorithms and constraint satisfaction algorithms.

Generating autonomous time-varying virtual cities

We propose an approach to generating virtual cities that vary dynamically over time, focusing on the layout of artificial elements such as building, roads, and traffic lights. We first define an environment vector as the amount of features reflecting economic and functional activities of citys residents in each block surrounded by roads. Our method generates virtual cities by deleting and locating buildings from two points of view: building layouts using environment vectors, which can represent features, themselves to generate cityscapes, and time-varying using changes of vectors to vary cityscapes. We introduce three modules of our city model briefly, and describe how our system relocates buildings in each block. In addition, we demonstrate that our method can represent features and generate various cityscapes that vary over time.

A composition algorithm for very hard graph 3-Colorability instances

Graph colorability (COL) is a constraint satisfaction problem, which has been studied in the context of computational complexity and combinatorial search algorithms. It is also interesting as subjects of heuristics[2]. Many research reports discuss the complexity of COL [2,3,4,8,9,10]. Examples of possible candidates of order parameters that explain the mechanism making COLs very hard include the 3-paths[10], the minimal unsolvable subproblems[8], and the frozen developments[4]. Instead of generate-and-test approaches, we propose a constructive approach producing 3-colorablity problems (3COLs) that are exceptionally hard for usual backtracking algorithms adopting Brelaz heuristics and for Smallk coloring program[1]. Instances generated by our procedure (1) are 4-critical, (2) include no near-4-cliques(n4cs; 4-cliques with 1 edge removed) as subgraphs, and (3) have the degree of every node limited to 3 or 4: quasi-regular. n nThis research was supported in part by the Ministry of Education, Culture, Sports, Science and Technology of Japan, Grant-in-Aid for Scientific Research (B)(2), No. 14380134, 2002-2005.

Interactive Japanese-to-braille translation using case-based knowledge on the web

We propose an interactive system for translating Japanese into BraiUe on the Web. Accurate automatic translation is difficult due to the ambiguous, complicated translation rules. Braille expressions must be made consistent throughout a text, even if a translation can be interpreted in more than one way. Braille translation productivity is slowed by the need for user intervention. Our system provides interactive Japaneseto-BraiUe translation and updates the knowledge base to keep results consistent and improve translation accuracy. Experimentals show that case acquisition reduces errors and that the user interface reduces output instability without requiring that the whole document be rechecked.

Updating building layouts of time-varying virtual cities

We propose an approach to generating virtual cities that vary dynamically over time, focusing on the layout of artificial elements such as building, roads, and traffic lights. We first define an environment vector as the amount of features reflecting economic and functional activities of citys residents in each block surrounded by roads. Our method generates virtual cities by deleting and locating buildings from two points of view: building layouts using vectors themselves to generate cityscapes, and time-varying using changes of vectors to vary cityscapes. We demonstrate that our method can represent features and generate various cityscapes that vary over time

Analysis of phase transitions in graph-coloring problems based on constraint structures

Situations very similar to phase transitions (PTs) have been observed in constraint satisfaction problems. In our analysis, applying the backtracking-based tree search algorithm with Brelaz heuristic to the graph-coloring problems with three colors (3GCPs), we first reconfirmed PT phenomena. We then traced the backtracking history for variables for which thrashing appears to occur in the hardest problems. As a result, we found a local key structure of a graph, or a rigid pair, which is a pair of nodes to each of which the same color must be assigned, and is included in a subgraph such as Fig. l(a) in 3GCPs. We found many rigid pairs in extraordinarily hard problems, in which very heavy trial-and-error repetitions of coloring are performed until the same color is assigned to rigid pairs.

Rearrangement of floor layouts based on constraint satisfaction

This paper describes a problem for rearranging floor layouts and proposes a system which generates a plan and schedule synchronously. Rearrangement of floor layout (RAFL) is a search problem, which consists of pre- and post-change layouts of objects, workers, and a work hour limit. The goal in solving RAFL is to find a pair of rearrangement plan and its schedule. RAFL deals with planning and scheduling simultaneously, whereas a schedule is usually determined after a plan is found. In RAFL, even if an optimal plan is obtained in advance, a schedule consisting of its elements may not be necessarily feasible. The proposed system uses constraints to represent the required knowledge and tree search algorithm. The system is interactive and informs the users of their search progress. The users may interrupt a search at any time to correct the system if the search is too slow or reaches an insufficient solution. Experimental results show that the system interacted with the user can find a valid solution in scores of minutes, where the time to solve is considerably reduced.