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.
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.
18603528
A Qualitative-Quantitative Methods-Based e-Learning Support System in Economic Education
This paper describes a new qualitative-quantitative simulator to help buyers learn how to make decisions when they purchase goods. In this paper, we propose an e-learning support system (LSDM) for assisting user decision making by applying artificial intelligence technology. When buyers purchase expensive items, they must carefully select these items from many alternatives. The learning support system provides useful information that assists consumers in purchasing goods. We employ qualitative simulations because the output simulation results are useful. Our system consists of a qualitative processing system and a quantitative calculation system. When users use the system, they first input information on the goods they want to purchase. The information input by users is used in the qualitative simulation. Next, they supply the details of their budgets, the rate of loans, and several other factors, on a form. The system then integrates the results of simulation and the user's input data and proposes plans to aid in their decision process. The system has several advantages: it can be used by simple input, the process of simulation is easy to understand, users can learn how to make decisions by trial and error, and the users can base their decision making on synthetic results.
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.
822028
An Approach to Coalition Formation Using Argumentation-Based Negotiation in Multi-agent Systems
In this paper, we propose an argumentation-based negotiation method for coalition formation. In existing argumentation method, it is difficult for an agent to calculate the effectiveness of each proposal, since agents are constructed based only on a logical framework. In our method, agents can calculate the effectiveness using a mechanism which can evaluate arguments. In order to evaluate the arguments, we prepare certain functions, so we employ the AHP. During the negotiation, agents can create the most effective proposal and change a negotiation strategy autonomously. An advantage of our method is that agents can reach an agreement reflecting user's multiple valuations, and the negotiation among agents is completed quickly. Another advantage is that if agents have no need to create proposals, each user's private data is not opened to others during the negotiation.
20000085
Toward a Large Scale E-Market: A Greedy and Local Search Based Winner Determination
Combinatorial auction is one of the most popular market mechanisms and it has a huge effect on electronic markets and political strategies. On large scale e-markets, we need a good approximation algorithm for winner determination that is robust for changing the distribution and the number of bids in an auction. We proposed approximate algorithms for combinatorial auctions with massively large number of (more than 100,000) bids. In this paper, we show the robustness of our winner determination algorithms for combinatorial auctions with large number of bids. Experimental results demonstrate that our proposed algorithms are robust on changing the distribution and the number of bids in an auction. Finally, we shortly describe a theoretical limitation about our algorithms that concerns with giving truthfulness of the auction mechanism.
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].