751173
Approximability of Partitioning Graphs with Supply and Demand
Suppose that each vertex of a graph G is either a supply vertex or a demand vertex and is assigned a positive real number, called the supply or the demand. Each demand vertex can receive “power” from at most one supply vertex through edges in G. One thus wishes to partition G into connected components so that each component C either has no supply vertex or has exactly one supply vertex whose supply is at least the sum of demands in C, and wishes to maximize the fulfillment, that is, the sum of demands in all components with supply vertices. This maximization problem is known to be NP-hard even for trees having exactly one supply vertex and strongly NP-hard for general graphs. In this paper, we focus on the approximability of the problem. We first show that the problem is MAXSNP-hard and hence there is no polynomial-time approximation scheme (PTAS) for general graphs unless P=NP. We then present a fully polynomial-time approximation scheme (FPTAS) for series-parallel graphs having exactly one supply vertex. The FPTAS can be easily extended for partial k-trees, that is, graphs with bounded treewidth.
43460576
Partitioning graphs of supply and demand
Assume that each vertex of a graph G is either a supply vertex or a demand vertex and is assigned a positive integer, called a supply or a demand. Each demand vertex can receive "power" from at most one supply vertex. One thus wishes to partition G into connected components by deleting edges from G so that each component C has exactly one supply vertex whose supply is no less than the sum of demands of all demand vertices in C. If G has no such partition, one wishes to partition G into connected components so that each component C either has no supply vertex or has exactly one supply vertex whose supply is no less than the sum of demands in C, and wishes to maximize the sum of demands in all components with supply vertices. We deal with such a maximization problem, which is NP-hard even for trees and strong NP-hard for general graphs. In this paper, we give a pseudo-polynomial-time algorithm to solve the problem for series-parallel graphs. The algorithm can be easily extended for partial k-trees, that is, graphs with bounded tree-width.
2226240
Partitioning Trees of Supply and Demand
Assume that a tree T has a number ns of "supply vertices" and all the other vertices are "demand vertices." Each supply vertex is assigned a positive number called a supply, while each demand vertex is assigned a positive number called a demand. One wish to partition T into exactly ns subtrees by deleting edges from T so that each subtree contains exactly one supply vertex whose supply is no less than the sum of demands of all demand vertices in the subtree. The "partition problem" is a decision problem to ask whether T has such a partition. The "maximum partition problem" is an optimization version of the partition problem. In this paper, we give three algorithms for the problems. First is a linear-time algorithm for the partition problem. Second is a pseudo-polynomial-time algorithm for the maximum partition problem. Third is a fully polynomial-time approximation scheme (FPTAS) for the maximum partition problem.
10045838
Algorithms for finding distance-edge-colorings of graphs
For a bounded integer @?, we wish to color all edges of a graph G so that any two edges within distance @? have different colors. Such a coloring is called a distance-edge-coloring or an @?-edge-coloring of G. The distance-edge-coloring problem is to compute the minimum number of colors required for a distance-edge-coloring of a given graph G. A partial k-tree is a graph with tree-width bounded by a fixed constant k. We first present a polynomial-time exact algorithm to solve the problem for partial k-trees, and then give a polynomial-time 2-approximation algorithm for planar graphs.
40835687
Partitioning trees of supply and demand
Assume that a tree T has a number ns of "supply vertices" and all the other vertices are "demand vertices." Each supply vertex is assigned a positive number called a supply, while each demand vertex is assigned a positive number called a demand. One wishes to partition T into exactly ns subtrees by deleting edges from T so that each subtree contains exactly one supply vertex whose supply is no less than the sum of demands of all demand vertices in the subtree. The "partition problem" is a decision problem to ask whether T has such a partition. The "maximum partition problem" is an optimization version of the partition problem. In this paper, we give three algorithms for the problems. The first is a linear-time algorithm for the partition problem. The second is a pseudo-polynomial-time algorithm for the maximum partition problem. The third is a fully polynomial-time approximation scheme (FPTAS) for the maximum partition problem.
32325022
Algorithms for Finding Distance-Edge-Colorings of Graphs
For a bounded integer l, we wish to color all edges of a graph G so that any two edges within distance l have different colors. Such a coloring is called a distance-edge-coloring or an l-edge-coloring of G. The distance-edge-coloring problem is to compute the minimum number of colors required for a distance-edge-coloring of a given graph G. A partial k-tree is a graph with tree-width bounded by a fixed constant k. We first present a polynomial-time exact algorithm to solve the problem for partial k-trees, and then give a polynomial-time 2-approximation algorithm for planar graphs.
40274616
On the spectra of certain distance-regular graphs
Let r be an undirected graph whose vertex-set V(F) is the set (ZJ~ , u2 ,..., v,>. The adjacency matrix of I’ is the n x n matrix A = A(r), over the complex number field, whose entries aij are given by a,j = 1 if vi and vi are adjacent, = 0 otherwise. DEFINITION 1. The spectrum of r is the set of distinct eigenvalues 4l , 4 ,**-> Od of A(F), together with their multiplicities, written m(&), m(4),..., m(0,). Since r is undirected, A is symmetric, and so the Bi are all real numbers. We arrange the Bi in increasing order, namely, 0, < O1 < *.. < e dMany studies have been done on the spectra of graphs by many mathematicians. Some of them may be found, for instance, in Biggs [2].
35506309
Scheduling Meetings with Distributed Local Consistency Reinforcement
8383423
A Support Method for Qualitative Simulation-Based Learning System
In this paper, we mainly present a support method of our proposed e-learning system. We employ qualitative simulations because this lets the learners understand the conceptual principles in economic dynamics. First, we define some qualitative values employed on simulation graph model that consists of nodes and arcs. Then, we show the support method using our learning system based on qualitative simulation.
204985889
Regular graphs with excess one
Abstract It is shown that there exists no regular graph with excess e =1 and girth 2 r +1⩾5.
13087182
A Logic-based Framework for Mobile Intelligent Information Agents
Information agents are computational software systems that provides transparent access to many different information sources in the Internet, and to be able to retrieve, analyze, manipulate, and integrate heterogeneous data and information on demand. Mobile agents are an effective choice for many applications to improve latency and bandwidth of client-server applications and to reduce vulnerability to network disconnection. In this paper, we propose MiLog, a logic-based mobile agent framework for constructing intelligent information agents. In the framework, inference and planning process of an agent is written in a compact logic program. A new generation logic program execution engine provides strong migration capability with reasonable execution speed. The framework has been used to develop a web-based decision support system ’BiddingBot’.