|
House Allocation Problem
In economics and computer science, the house allocation problem is the problem of assigning objects to people with different preferences, such that each person receives exactly one object. The name "house allocation" comes from the main motivating application, which is assigning dormitory houses to students. Other commonly used terms are assignment problem and one-sided matching. When agents already own houses (and may trade them with other agents), the problem is often called a housing market. In house allocation problems, it is assumed that monetary transfers are not allowed; the variant in which monetary transfers are allowed is known as rental harmony. Definitions There are ''n'' people (also called: ''agents''), and m objects (also called: ''houses''). The agents may have different preferences over the houses. They may express their preferences in various ways: * ''Binary valuations'': each agent values each house at either 1 (which means that the agent likes the house), or ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Legislative Chamber
A legislative chamber or house is a deliberative assembly within a legislature which generally meets and votes separately from the legislature's other chambers. Legislatures are usually unicameral, consisting of only one chamber, or bicameral, consisting of two, but there are rare examples of tricameral and tetracameral legislatures. The Socialist Federal Republic of Yugoslavia is the only country documented as having a pentacameral (later hexacameral) legislature. Bicameralism In a ''bicameral'' legislature, the two bodies are often referred to as an ''upper'' and a ''lower'' house, where the latter is often regarded as more particularly the representatives of the people. The lower house is almost always the originator of legislation, and the upper house is the body that offers the "second look" and decides whether to veto or approve the bills. In the United Kingdom legislation can be originated in either house, but the lower house can ultimately prevail if the t ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Bipartite Graph
In the mathematics, mathematical field of graph theory, a bipartite graph (or bigraph) is a Graph (discrete mathematics), graph whose vertex (graph theory), vertices can be divided into two disjoint sets, disjoint and Independent set (graph theory), independent sets U and V, that is, every edge (graph theory), edge connects a Vertex (graph theory), vertex in U to one in V. Vertex sets U and V are usually called the ''parts'' of the graph. Equivalently, a bipartite graph is a graph that does not contain any odd-length cycle (graph theory), cycles. The two sets U and V may be thought of as a graph coloring, coloring of the graph with two colors: if one colors all nodes in U blue, and all nodes in V red, each edge has endpoints of differing colors, as is required in the graph coloring problem.. In contrast, such a coloring is impossible in the case of a non-bipartite graph, such as a Gallery of named graphs, triangle: after one node is colored blue and another red, the third vertex ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Assignment Problem
The assignment problem is a fundamental combinatorial optimization problem. In its most general form, the problem is as follows: :The problem instance has a number of ''agents'' and a number of ''tasks''. Any agent can be assigned to perform any task, incurring some ''cost'' that may vary depending on the agent-task assignment. It is required to perform as many tasks as possible by assigning at most one agent to each task and at most one task to each agent, in such a way that the ''total cost'' of the assignment is minimized. Alternatively, describing the problem using graph theory: :The assignment problem consists of finding, in a weighted graph, weighted bipartite graph, a Matching (graph theory), matching of maximum size, in which the sum of weights of the edges is minimum. If the numbers of agents and tasks are equal, then the problem is called balanced assignment, and the graph-theoretic version is called minimum-cost perfect matching. Otherwise, it is called unbalanced assig ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Equitable Division
Equitable (EQ) cake-cutting is a kind of a fair cake-cutting problem, in which the fairness criterion is equitability. It is a cake-allocation in which the subjective value of all partners is the same, i.e., each partner is equally happy with his/her share. Mathematically, that means that for all partners and : :V_i(X_i) = V_j(X_j) Where: *X_i is the piece of cake allocated to partner ; *V_i is the value measure of partner . It is a real-valued function that, for every piece of cake, returns a number that represents the utility of partner from that piece. Usually these functions are normalized such that V_i(\emptyset)=0 and V_i(EntireCake)=1 for every . See the page on equitability for examples and comparison to other fairness criteria. Finding an equitable cake-cutting for two partners One cut - full revelation When there are 2 partners, it is possible to get an EQ division with a single cut, but it requires full knowledge of the partners' valuations. Assume that the cake i ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
