Eiji Miyano

Intractability of read-once resolution

Read-once resolution (ROR) is a resolution proof system in which the rule (A+x)(B+.

Approximating maximum diameter-bounded subgraphs

The paper studies the maximum diameter-bounded subgraph problem (MaxDBS for short) which is defined as follows: Given an n-vertex graph G and a fixed integer d≥1, the goal is to find its largest subgraph of the diameter d. If d=1, the problem is identical to the maximum clique problem and thus it is

NP-hardness of the sorting buffer problem on the uniform metric

{\cal NP}

Degree-Constrained Graph Orientation: Maximum Satisfaction and Minimum Violation

-hard to approximate MaxDBS to within a factor of n1−e for any e>0. Also, it is known to be

Approximation Algorithms for the Graph Orientation Minimizing the Maximum Weighted Outdegree

{\cal NP}

Pickup and delivery for moving objects on broken lines

-hard to approximate MaxDBS to within a factor of n1/3−e for any e>0 and a fixed d≥2. In this paper, we first strengthen the hardness result; we prove that, for any e>0 and a fixed d≥2, it is

Three-Dimensional Meshes are Less Powerful than Two-Dimensional Ones in Oblivious Routing

{\cal NP}

The Bump Hunting Method Using the Genetic Algorithm with the Extreme-Value Statistics

-hard to approximate MaxDBS to within a factor of n1/2−e. Then, we show that a simple polynomial-time algorithm achieves an approximation ratio of n1/2 for any even d≥2, and an approximation ratio of n2/3 for any odd d≥3. Furthermore, we investigate the (in)tractability and the (in)approximability of MaxDBS on subclasses of graphs, including chordal graphs, split graphs, interval graphs, and k-partite graphs.

Routing Problems on the Mesh of Buses

An instance of the sorting buffer problem (SBP) consists of a sequence of requests for service, each of which is specified by a point in a metric space, and a sorting buffer which can store up to a limited number of requests and rearrange them. To serve a request, the server needs to visit the point where serving a request p following the service to a request q requires the cost corresponding to the distance d(p,q) between p and q. The objective of SBP is to serve all input requests in a way that minimizes the total distance traveled by the server by reordering the input sequence. In this paper, we focus our attention to the uniform metric, i.e., the distance d(p,q)=1 if p q, d(p,q)=0 otherwise, and present the first NP-hardness proof for SBP on the uniform metric.

GRAPH ORIENTATION TO MAXIMIZE THE MINIMUM WEIGHTED OUTDEGREE

A degree-constrained graph orientation of an undirected graph G is an assignment of a direction to each edge in G such that the outdegree of every vertex in the resulting directed graph satisfies a specified lower and/or upper bound. Such graph orientations have been studied for a long time and various characterizations of their existence are known. In this paper, we consider four related optimization problems introduced in reference (Asahiro et al. LNCS 7422, 332–343 (2012)): For any fixed non-negative integer W, the problems MAXW-LIGHT, MINW-LIGHT, MAXW-HEAVY, and MINW-HEAVY take as input an undirected graph G and ask for an orientation of G that maximizes or minimizes the number of vertices with outdegree at most W or at least W. As shown in Asahiro et al. LNCS 7422, 332–343 (2012)).