PPT-Stable Matchings Given two sets

each agent ranks every agent in the other set Goal Match each agent to exactly one agent in the other set respecting their preferences How do we respect preferences Avoid blocking pairs. A . set. is an unordered collection of objects, called . elements. of the set. A set is said to . contain. its elements. If S and T are sets, and (x S) ->(x T) then we say that S is a . subset. Leonardo de Moura and Nikolaj . Bjørner. Microsoft Research. What. EPR . . . Deciding EPR using DPLL + Substitution sets. Why? EPR is the next SAT. SAT .  EPR. Deciding EPR using DPLL + Substitution sets. D. K. Bhattacharya. Set. It . is just things grouped together with a . certain property in . common. . Formally it is defined as a collection of . well defined objects. , so that given an object we should be able to say whether it is a member of the set or not.. Finding the . Clar. number and the Fries number of a . benzenoid. in polynomial time using a LP.. The desired solutions are integer but it has been proven that the basic feasible solutions are all integral so integer programming tactics are not required.. Numbers . Integers . Rational. . Numbers. Real Numbers . ℝ. . . Insert . each of the following numbers in . the . correct place on the diagram. :. 5. . , . 6.. , 2. ,. -3, . , 0 and -. . .  . Algorithms. and Networks 2014/2015. Hans L. . Bodlaender. Johan M. M. van Rooij. A Prize Winning Algorithm. Lloyd Shapley, Nobel Prize Winner 2012 in economics.. Obtained the prize for a number of contributions, one being the Gale-Shapley algorithm, discussed today.. Use set notation and terminology.. List elements of a finite set.. Describe the rule that defines a set.. Describe and recognise equality of sets.. Perform intersection, union.. Investigate commutativity for intersection and union.. A set is an object defined as a collection of other distinct objects, known as elements of the set. The elements of a set can be anything: people, plants, numbers, functions, and even other sets.. Using sets, nearly any mathematical concept can be derived. Gerry Shea, Michael . Bailit. , Christine Hughes, and Susan . Schow. February 24, 2015. Welcome and Introduction. 2. Gerry Shea. Buying Value Project . Director. gshea@buyingvalue.org. 202 256-7577. www.buyingvalue.org. . unordered, no duplicate. If S is a set, then. “x .  S” means x is an element of S. “x  S” means x is not an element of S. Set-roster. notation. :. S = {1, 2, 3}. S = {1, 2, …, 100}. Rodney G. Roberts. Anthony . Maciejewski. Presenter: . Karthik. . Sheshadri. Introduction. =J. Solution is of the form. , with JG=I.. For a repeatable strategy, no end effector movement => no joint movement.. Section. . 2.4. Cardinality. How can we compare the sizes of two sets?. If . S. = {. x.  . .   .  . : . x. 2. = 9}, then . S.  = {–3,.  . 3} and we say that . S. has two elements.. (A Case Study). Based on joint works with: . Rachel Cummings, Justin Hsu, . Zhiyi. Huang, . Sampath. Kannan, Michael Kearns, . Mallesh. . Pai. , Jamie Morgenstern, Ryan Rogers, Tim . Roughgarden. Jon Ullman, and Steven Wu. Gale-Shapley Algorithm. Christian Reyes. Enrique Treviño. Think About…. Imagine…. Finally…. Outline. Stable Matching and the Stable Marriage Problem. Richter Matching. What Next?. Stable Matching.