70 research outputs found
On the Equivalence between some Local and Global Chinese Postman and Traveling Salesman Graphs
A connected graph G=(V,E), a vertex in V and a non-negative weight function defined on Ecan be used to induce Chinese postman and traveling salesman (cooperative) games. A graph G=(V,E) is said to be locally (respectively, globally) Chinese postman balanced (respectively, totally balanced, submodular) if for at least one vertex (respectively, for all vertices) in V and any non-negative weight function defined on E, the corresponding Chinese postman game is balanced (respectively, totally balanced, submodular). Local and global traveling salesman balanced (respectively, totally balanced, submodular) graphs are similarly defined. In this paper we study the equivalence between local and global Chinese postman balanced (respectively, totally balanced, submodular) graphs, and between local and global traveling salesman submodular graphs.
Operations Research Games: A Survey
This paper surveys the research area of cooperative games associated with several types of operations research problems in which various decision makers (players) are involved.Cooperating players not only face a joint optimisation problem in trying, e.g., to minimise total joint costs, but also face an additional allocation problem in how to distribute these joint costs back to the individual players.This interplay between optimisation and allocation is the main subject of the area of operations research games.It is surveyed on the basis of a distinction between the nature of the underlying optimisation problem: connection, routing, scheduling, production and inventory.cooperative games;operational research
On Games Arising From Multi-Depot Chinese Postman Problems
This paper introduces cooperative games arising from multi-depot Chinese postman problems and explores the properties of these games. A multi-depot Chinese postman problem (MDCP) is represented by a connected (di)graph G, a set of k depots that is a subset of the vertices of G, and a non-negative weight function on the edges of G. A solution to the MDCP is a minimum weight tour of the (di)graph that visits all edges (arcs) of the graph and that consists of a collection of subtours such that the subtours originate from dierent depots, and each subtour starts and ends at the same depot. A cooperative Chinese postman (CP) game is induced by a MDCP by associating every edge of the graph with a dierent player. This paper characterizes globally and locally k-CP balanced and submodular (di)graphs. A (di)graph G is called globally (locally) k-CP balanced (respectively submodular), if the induced CP game of the corresponding MDCP problem on G is balanced (respectively submodular) for any (some) choice of the locations of the k depots and every non-negative weight function
Chinese postman games with multi-located players
This paper analyses Chinese postman games with multi-located players, which generalize Chinese postman games by dropping the one-to-one relation between edges and players. In our model, we allow players to be located on more than one edge, but at most one player is located on each edge. The one-to-one relation between edges and players is essential for the equivalence between Chinese postman-totally balanced and Chinese postman-submodular graphs shown in the literature. We illustrate the invalidity of this result in our model. Besides, the location of the post office has a relevant role in the submodularity and totally balancedness of Chinese postman games with multi-located players. Therefore, we focus on sufficient conditions on the assignment of players to edges to ensure submodularity of Chinese postman games with multi-located players, independently of the associated travel costs. Moreover, we provide some insights on the difficulty of finding necessary conditions on assignment functions to this end
Engineering an Approximation Scheme for Traveling Salesman in Planar Graphs
We present an implementation of a linear-time approximation scheme for the traveling salesman problem on planar graphs with edge weights. We observe that the theoretical algorithm involves constants that are too large for practical use. Our implementation, which is not subject to the theoretical algorithm\u27s guarantee, can quickly find good tours in very large planar graphs
Cost allocation in connection and conflict problems on networks: a cooperative game theoretic approach
This thesis examines settings where multiple decision makers with conflicting interests
benefit from cooperation in joint combinatorial optimisation problems. It draws on cooperative game theory, polyhedral theory and graph theory to address cost sharing in
joint single-source shortest path problems and joint weighted minimum colouring problems.
The primary focus of the thesis are problems where each agent corresponds to a
vertex of an undirected complete graph, in which a special vertex represents the common supplier. The joint combinatorial optimisation problem consists of determining the
shortest paths from the supplier to all other vertices in the graph. The optimal solution
is a shortest path tree of the graph and the aim is to allocate the cost of this shortest
path tree amongst the agents. The thesis defines shortest path tree problems, proposes
allocation rules and analyses the properties of these allocation rules. It furthermore introduces shortest path tree games and studies the properties of these games. Various core
allocations for shortest path tree games are introduced and polyhedral properties of the
core are studied. Moreover, computational results on finding the core and the nucleolus
of shortest path tree games for the application of cost allocation in Wireless Multihop
Networks are presented.
The secondary focus of the thesis are problems where each agent is interested in
having access to a number of facilities but can be in conflict with other agents. If two
agents are in conflict, then they should have access to disjoint sets of facilities. The
aim is to allocate the cost of the minimum number of facilities required by the agents
amongst them. The thesis models these cost allocation problems as a class of cooperative
games called weighted minimum colouring games, and characterises total balancedness
and submodularity of this class of games using the properties of the underlying graph
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