PPT-Data Structures for Disjoint Sets

Manolis Koubarakis Data Structures and Programming Techniques 1 Dynamic Sets Sets are fundamental for mathematics but also for computer science In computer science we usually study dynamic sets . A minimum spanning tree is a connected subgraph of G that spans all vertices at minimum cost The number of edges in the minimum spanning tree is Figure 6b is the minimum spanning tree of the graph in Figure 6a In this case the minimum spanning tree Farscape Thanks for Sharing June 15 2001 What rolls down stairs alone or in pairs rolls over your neighbors dog Whats great for a snack and ts on your back Its Log Log Log Its Log Its Log Its big its heavy its wood Its Log Its Log Its better than b entities relationships lang. ISA disjoint covering ISA disjoint covering complexity C1vC2 C1uC2v? C=C1tC2 R1vR2 R1uR2v? R=R1tR2 ERfull + + + + + + EXPTIME[5] ERisaR + + + + EXPTIME ERbool + + + NP ERr Grid-Minor Theorem. Chandra . Chekuri. , . Julia Chuzhoy. UIUC. . TTIC. Grid Minor Theorem . (Excluded Grid Theorem). [Robertson, Seymour ‘86]. Graph Minor Theory . [Robertson – Seymour]. 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.. 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. and Matrices. Chapter 2. With Question/Answer Animations. Copyright © McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill . . 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}. Noemi Derzsy. What is a Dominating Set?. Definition. : . a subset . S. of nodes of a network such that each node not in . S . is adjacent to at least one node from . S . (. NP-hard. problem. ). Why the interest in dominating sets?. webbasis. Using the. DART Application. How to Create Employee Sets. Possible Uses of Creating Employee Sets. . This is a great tool to use when you want to display cost centers for an employee in a report type format for ease of viewing and locating information.. Homologous structures. Human Arm . Bat Wing . Whale Flipper. . Analogous. Structures . Similar functions but NOT structurally related. . Insects are arthropods and birds are vertebrates. . The wing of a bird and the wing of a butterfly are examples of .