6670892
Partitioning a graph of bounded tree-width to connected subgraphs of almost uniform size
Abstract Assume that each vertex of a graph G is assigned a nonnegative integer weight and that l and u are nonnegative integers. One wishes 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 ) -partition. We deal with three problems to find an ( l , u ) -partition of a given graph; the minimum partition problem is to find an ( l , u ) -partition with the minimum number of components; the maximum partition problem is defined analogously; and the p-partition problem is to find an ( l , u ) -partition with a fixed number p of components. All these problems are NP-complete or NP-hard, respectively, 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 ( u 4 n ) and the p-partition problem can be solved in time O ( p 2 u 4 n ) for any series-parallel graph with n vertices. The algorithms can be extended for partial k-trees, that is, graphs with bounded tree-width.
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.
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.
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.
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.
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.
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.
15889327
Towards Better Approximation of Winner Determination for Combinatorial Auctions with Large Number of Bids
We propose new approximate algorithms for combinatorial auctions with massively large number of (more than 100,000) bids. In this paper, we focus on a more practical approximated algorithm in the context of revenue maximization. We propose a hill-climbing greedy algorithm, a SA-like random search algorithm, and their enhancement for searching multiple key parameter values. The experimental results demonstrate that our algorithms perform approximately 0.997 optimality compared with the optimal solutions and better than previously presented approximated algorithms. We also demonstrate that our algorithms are a kind of anytime algorithm that bring better results in shorter computational time that can be applied to large and dynamic electronic markets.
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.
35506309
Scheduling Meetings with Distributed Local Consistency Reinforcement