3208882
Partitioning a Weighted Graph to Connected Subgraphs of Almost Uniform Size
Assume that each vertex of a graph G is assigned a nonnegative integer weight and that l and u are nonnegative integers. One wish to partition G into connected components by deleting edges from G so that the total weight of each component is at least l and at most u. Such an “almost uniform” partition is called an $(l, u) \mbox{-}$partition. We deal with three problems to find an $(l, u) \mbox{-}$partition of a given graph. The minimum partition problem is to find an $(l, u) \mbox{-}$partition with the minimum number of components. The maximum partition problem is defined similarly. The p-partition problem is to find an $(l, u) \mbox{-}$partition with a fixed number p of components. All these problems are NP-complete or NP-hard even for series-parallel graphs. In this paper we show that both the minimum partition problem and the maximum partition problem can be solved in time O(u4n) and the p-partition problem can be solved in time O(p2u4n) for any series-parallel graph of n vertices. The algorithms can be easily extended for partial k-trees, that is, graphs with bounded tree-width.
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.
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.
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.
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.
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’.
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.
5841312
Coalition Formation among Agents in Complex Problems Based on a Combinatorial Auction Perspective
AbstrAct This chapter focuses on a scheduling problem that considers various constraints as a complex real-world problem. Constraints on scheduling can be expressed as combinations of items (time slots) in a combinatorial auction. Agents bid for necessary combinations of time slots to satisfy users' preferences. We formalize a combinatorial auction for scheduling as an MIP (mixed integer programming) problem, which integrates the constraints on items and bids to express complex problems. This integration solves the trade-off between the computation time to find the solution and the expressiveness to represent a scheduling problem. This chapter presents a new formalization of a combinatorial auction with constraints. We have experimentally confirmed that our method can obtain a socially preferable schedule in practical time.
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.