# Ppt on space complexity

##### Complex Networks1 A short course on complex networks Anthony Bonato Ryerson University MITACS Workshop On Social Networks August 9, 2010.

, b, d, D), dimension of an OSN gives smallest number of attributes needed to identify users that is, given the graph structure, we can (theoretically) recover the social space Complex Networks100 6 Dimensions of Separation OSNDimension YouTube6 Twitter4 Flickr4 Cyworld7 Complex Networks101 Future directions what precisely is a community in an OSN? could help us with applications such as targeted advertising and counterterrorism/

##### CS 3813: Introduction to Formal Languages and Automata Chapter 14 An Introduction to Computational Complexity These class notes are based on material from.

-hard by showing that another NP-hard problem is polynomial- time reducible to it. (This establishes a lower bound on the complexity of the problem.) Complexity classes A complexity class is a class of problems grouped together according to their time and/or space complexity NC: can be solved very efficiently in parallel P: solvable by a DTM in poly-time (can be solved efficiently/

##### Theory of Computational Complexity Yuji Ishikawa Avis lab. M1.

the maximum number of tape cells that M scans on any input of length n If the space complexity of M is f(n), we say that M runs in space f(n) Space Complexity accept Computation tree of a DTM …... f(n) : max number of used cells q/Theorem, PSPACE = NPSPACE, because the square of a polynomial function is still a polynomial. Outline Chapter 8 ： Definition of Space Complexity Savitch’s Theorem The Class PSPACE PSPACE-Completeness TQBF Problem PSPACE-Completeness Definition 8.8 A language B is PSPACE-complete if/

##### 1 STATE-SPACE SEARCH 159.302 STATE-SPACE SEARCH Motivation and Background 159302 Uninformed Search, Informed Search, Any-Path Search, Optimal Search Source.

the “depth” parameter. This is the bottom-line irreducible worst case cost of systematic searches. 131SEARCH Worst Case Complexity 4 The number of states in the search space may be exponential in some “depth” parameter, e.g. number of actions in a plan, number of /of what states have been visited (expanded), searches can do (much) worse than visit every state. 132SEARCH Worst Case Complexity 4 N NA state space with N states may give rise to a search tree that has a number of nodes that is exponential in N,/

##### T HE R EGIME C OMPLEX OF S PACE W ARFARE : A R OADMAP TO G OVERNANCE Dr. Eytan Tepper DCL candidate & Erin J.C. Arsenault Fellow in Space Governance

other” The result: multiple normative frameworks and operative mechanisms (overlapping, competing, complementing) Mapping the regime complex of space warfare Mapping: normative framework: principles, norms, rules, decision-making procedures (all  ”norms”) Noting:/UNGA resolutions & Sino-Russian draft treaty on prevention of weaponization. Mechanisms = COPUOS, ITU Mapping the regime complex of space warfare Theater of cyberspace: norms = UN Group of Governmental Experts (GGE) – report + recommendations of /

#####  2005 SDU Lecture14 Mapping Reducibility, Complexity.

N, where f(n) is the maximum number of steps that M uses on any branch of its computation on any input of length n. The space complexity of M is the function f: N  N, where f(n) is the maximum number of tape cells that M scans on any branch of / g(n) = O(f (n)), if there exist constant n 0 and c such that for all n  n 0, g(n)  cf(n)  Space complexity classes can be defined similarly.  2004 SDU 15 Relationship among models Theorem. For every t(n)  n, each t(n) time multi-tape Turing machine has an /

##### Computational Complexity Theory Lecture 1: Intro; Turing machines; Class P and NP Indian Institute of Science.

that has exactly one or no satisfying assignment? Structural Complexity Classes P, NP, NP-completeness. Space bounded computation. Structural Complexity Classes P, NP, NP-completeness. Space bounded computation. How much space is required to check s-t connectivity? Structural Complexity Classes P, NP, NP-completeness. Space bounded computation. Counting complexity. Structural Complexity Classes P, NP, NP-completeness. Space bounded computation. Counting complexity. How hard is it to count the number of/

##### Hidden Metric Spaces and Navigability of Complex Networks

2009 Result #3: Successful greedy paths are shortest Regardless the structure of the hidden space, complex network topologies are such, that all successful greedy paths are asymptotically shortest But: how many greedy paths are successful /geometry of trees; the volume of balls grows exponentially with their radii Greedy routing in complex networks, including the real AS Internet, embedded in hyperbolic spaces, is always successful and always follows shortest paths Even if some links are removed, emulating/

##### Lets Give More Emphasis to Opportunities in Complex Enterprise Environments Brian E. White, Ph.D. Director, Systems Engineering Process Office The MITRE.

. The developmental regime is associated with changes in the system. These two regimes cannot be sufficiently isolated for a complex-system. n Identify or define targeted outcome spaces: Outcome spaces are large sets of possible partial outcomes at specific scales and in specific regimes. The complex-system itself will choose the exact combinations of partial outcomes that it realizes. n Establish rewards (and penalties/

##### The Practical Application of Complexity Theory in the Public and Private Sector Exploring the Science of Complexity in Aid Policy and Practice at ODI on.

them unintentionally However, not enough to name and describe the concepts Can use the logic of complexity to: a. Understand the problem space when addressing apparently intractable problems b. Create enabling environments How & Whom? Policy makers who become/ workshop with all interviewers and sponsors 2-day Workshop to Identify the Problem Space 72 themes grouped into 8 clusters: OBU/CFBU Interface Complexity of structure (matrix) Human behaviours Cultures* Communication Leadership/role of central team/

##### Attractor neural networks and concept formation in psychological spaces: mind from brain? Włodzisław Duch Department of Informatics, Nicholas Copernicus.

Ohm’s & 2 Kirhoff’s. All laws A=B+C, A=B×C , A-1=B-1+C-1, have identical geometric interpretation! 13 true, 14 false facts; simple P-space, complex neurodynamics. Intuitive reasoning 5 laws are simultaneously fulfilled, all have the same representation: Question: If R2=+, R1=0 and V =0, what can be said about I, V1, V2 ? Find/

: There are n nodes in the list All data references are null Number of references in the list and space required: Required space Total Reference SizeOfSinglyLinkedListElementReference 1 head tail n*SizeOfSinglyLinkedListElementReference n next n*SizeOfObjectReference data Total space = (n + 2)*SizeOfSinglyLinkedListElementReference + n*SizeOfObjectReference Hence space complexity is O(n) List Creation An empty list is created as follows: Once created, elements can be inserted into/

##### © 2004 The MITRE Corporation. All rights reserved Engineering a Complex System: The Air & Space Operations Center (AOC) as a Complex Systems Exemplar Doug.

© 2004 The MITRE Corporation. All rights reserved Engineering a Complex System: The Air & Space Operations Center (AOC) as a Complex Systems Exemplar Doug Norman Senior Technical Advisor, AOC-WS Dept Head, AF Battle Management / and – respond to conditions as they emerge n Guides garden into the desired outcome space Sounds like a complexity problem? © 2004 The MITRE Corporation. All rights reserved SDM 2004 What is Complexity? n A measure of potentiality n It does not mean Difficult to understand n Contrast/

##### Units of Play (Simple, Complex, Super Units)

purpose usually does not have subparts e.g. a drum, a spinning toy, a windup toy = one play space (when calculating the complexity of the play environment) Shipley, D. (1993). Empowering children: Play-based curriculum for lifelong learning. Scarborough, Ont. : Nelson Canada / acceptable for the age group: 1-2 years = 5-6 play space? 3-4 years = 3-4 play space? 5-6 years = 2-3 play space? Is there a need for: More simple units? More complex units? More super units? Is there a need to combine units? /

##### Topic Number 2 Efficiency – Complexity Algorithm Analysis " bit twiddling: 1. (pejorative) An exercise in tuning (see tune) in which incredible amounts.

other types –often able to trade SPACE for TIME. –Faster solution that uses more space –Slower solution that uses less space CS 314Efficiency - Complexity 30 Big O Space  Big O could be used to specify how much space is needed for a particular algorithm –/if willing to take longer –truly beautiful solutions take less time and space The biggest difference between time and space is that you cant reuse time. - Merrick Furst CS 314Efficiency - Complexity 31 Quantifiers on Big O  It is often useful to discuss/

##### D-Theory - Model of cell-structured space

and of the three families of particles were defined. It was shown that the electromagnetic fields are caused by the effects of the complex space and that the model is compatible with the Maxwells equations This is the version v2.12 published 14.4.2014. email: virtanen./expanding speed or the cosmic multiplier a is less than R /  and spirals cut each other in point C. Thus both complex spaces seem to have there a common point. The light trace at the spiral causes such an effect that the points of the curve/

##### Time-Space Tradeoffs in Resolution: Superpolynomial Lower Bounds for Superlinear Space Chris Beck Princeton University Joint work with Paul Beame & Russell.

store only those. Hard to do well! Memory becomes a bottleneck. Question: Is this inherent? Or can the right heuristics avoid the memory bottleneck? Proof Complexity & Sat Solvers Proof Size ≤ Time for Ideal SAT Solver Proof Space ≤ Memory for Ideal SAT Solver Many explicit hard UNSAT examples known with exponential lower bounds for Resolution Proof Size. Question: Is this also true for/

##### Based on Powerpoint slides by Giorgi Japaridze, Villanova University Space Complexity and Interactive Proof Systems Sections 8.0, 8.1, 8.2, 8.3, 10.4.

of CANYIELD(c start, c accept, 2 df(n) ). ” Proof of Savitch ’ s theorem (iii) 8.1.d It remains to analyze the space complexity of M. Whenever CANYIELD invokes itself recursively, it stores the current stage number and the values of c 1,c 2 and p on a stack so/for M ’ to work properly) will only take O(log f(n)) space. And, while trying an i, M ’ uses no more additional space than M does. This space can be recyc- led on every iteration, so the space complexity of M ’ remains O(f 2 (n)). PSPACE defined 8.2.a /

##### Time-Space Tradeoffs in Resolution: Superpolynomial Lower Bounds for Superlinear Space Chris Beck Princeton University Joint work with Paul Beame & Russell.

store only those. Hard to do well! Memory becomes a bottleneck. Question: Is this inherent? Or can the right heuristics avoid the memory bottleneck? Proof Complexity & Sat Solvers Proof Size ≤ Time for Ideal SAT Solver Proof Space ≤ Memory for Ideal SAT Solver Many explicit hard UNSAT examples known with exponential lower bounds for Resolution Proof Size. Question: Is this also true for/

##### Peter van Emde Boas: Games and Complexity Guangzhou 2009 Complexity, Speed-up and Compression Games and Complexity Peter van Emde Boas Guangzhou 2009 ©

 k --->  ’  ’ =  3 Peter van Emde Boas: Games and Complexity Guangzhou 2009 Constant Factor Speed-up This yields automatic constant factor speed-up in space: Space( S(n) ) = Space( S(n)/k ) Snags: Input is not compressed! This may require additional steps and/diagonalization is possible Peter van Emde Boas: Games and Complexity Guangzhou 2009 SPACE COMPRESSION Downward Diagonalization If S 1 (n) > log(n) is space constructible and S 2 (n) = o(S 1 (n)) then Space( S 2 (n) )  Space( S 1 (n) ) On input i #/

##### Where is the Fastest Way Ahead to Understand & Design Complex Human Systems? The Multi-Agent-based Simulation Path R. H. Weber, Sr. P.E. The Aerospace.

to Understand & Design Complex Human Systems? The Multi-Agent-based Simulation Path R. H. Weber, Sr. P.E. The Aerospace Corporation (310) 336-5715 System & Operations Engineering Reference Model Military Utility Space-Based KEW * S/, innovation, adhocracy, organized “stovepipes” US neglect of intellectual infrastructure Maladaptive effects of Cold War on military-industrial complex Impact  Loss of US industrial/economic competitiveness at macro-system level EU Airbus Consortium (Catia) & Japan Toyota/

##### Combinatorial Problems III: The Next Level of Complexity Ashish Sabharwal Cornell University March 5, 2008 2nd Asian-Pacific School on Statistical Physics.

shortest path, … Recap: Complexity Hierarchy Easy Hard PH EXP #P-complete/hard: #SAT, sampling, probabilistic inference, … 5 What is PSPACE? P-SPACE: “Polynomial space” as opposed to polynomial time space: amount of “working memory” / “notepad space” that an algorithm has at/On the road to a whole new range of applications: Strategic decision making Performance guarantees in complex multi-agent scenarios Secure communication and data networks in hostile environments Robust logistics planning in adversarial /

##### Searching the search space graph

leaf at the RHS so DFS will expand all nodes (m is cutoff) =1 + b + b2+ ......... + b^m = O (b^m) Space Complexity how many nodes can be in the queue (worst-case)? at depth l < d we have b-1 nodes at depth d we have b nodes /d=5 d=cut-off DFS = 1+10+100,…,=111,111 IDS = 123,456 Ratio is Comments on Iterative Deepening Search Complexity Space complexity = O(bd) (since its like depth first search run different times) Time Complexity 1 + (1+b) + (1 +b+b2) + .......(1 +b+....bd) = O(bd) (i.e., asymptotically/

##### Space Efficient Alignment Algorithms Dr. Nancy Warter-Perez June 24, 2005.

bytes to represent the trace back matrix June 24, 2005Space Efficient Alignment Algorithms6 Simple Improvement for Scoring Matrix In reality, the space complexity of the scoring matrix is only linear, i.e., O(2*min(m,n)) = O(min(m,n)) O/(n,m)) – if m < n, switch the sequences (or save a row of s and s reverse instead) Linear space complexity!! June 24, 2005Space Efficient Alignment Algorithms10 Project Teams and Presentation Assignments (Revised) Base Project (Global Alignment): Miguel and Joseph Extension /

##### Evolution of Complex Systems Lecture 3: Theoretical foundations Peter Andras / Bruce Charlton

contingency Double contingency System identity System identity Identity violation and adaptation Identity violation and adaptation Complexity Complexity 3 Communication systems Communication system Communication units 4 Communication Sender unit: Signals generated Receiver unit/ rules: conditional probability distributions over the space of possible communications, which are part of the system Grammatical rules: conditional probability distributions over the space of possible communications, which are part /

##### Exploring the complexity limits of joint data detection and channel estimation Achilleas Anastasopoulos EECS Department, University of Michigan, Ann Arbor,

: two possible approaches 18 Approach A: Estimator-correlator Parameter estimator Parameter estimator Parameter estimator Estimator Metric Function Metric Function Metric Function Correlator arg max Obviously exponential complexity w.r.t. N 19 Approach B: Parameter space scan Known Parameter Detector Known Parameter Detector Known Parameter Detector Known Parameter Detector arg max Metric Function Metric Function Metric Function Metric Function Unfortunately, this method/

##### 1 Hybrid of search and inference: time- space tradeoffs chapter 10 ICS-275 Spring 2007.

K F H C B A L G J D F C B G D E treewidth = 2 cycle cutset = 5 Spring 2007 ICS-275 40 Time-Space complexity of of w-cutset Space: O(exp(w)) W -cutset: a set that when removed the induced- width is w. c(w): size of w-cutset. Time: O(exp(w/AO Search) 1.43.6 (Caching on Cutset) + (AO Search) 1.63.4 (Caching on Cutset) + (BE) 0.75.3 Spring 2007 ICS-275 73 Time-Space complexity of of w-cutset Space: O(exp(w)) W -cutset: a set that when removed the induced- width is w. c(w): size of w-cutset. m(w): depth of AO w-/

##### Ontologies Reasoning Components Agents Simulations Problem Solving through State Space Search Jacques Robin.

nodes  With such test  Depth-first, backtracking and iterative deepening search loose their linear worst- case space complexity,  for any guarantee to avoid all loops may require keeping an exponential number of expanded nodes in / search algorithms do not scale up,  neither theoretically (exponential worst case time or space complexity)  nor empirically (experimentally measured average case time or space complexity)  Heuristic search algorithms do scale up to very large problem instances, in some /

##### CS151 Complexity Theory Lecture 2 April 3, 2015. 2 Time and Space A motivating question: –Boolean formula with n nodes –evaluate using O(log n) space?

outputs exactly f(n) symbols on input 1 n, and runs in time O(f(n) + n) and space O(f(n)). April 3, 201520 Proper Complexity Functions includes all reasonable functions we will work with –log n, √n, n 2, 2 n, n!, /201521 Hierarchy Theorems Does genuinely more space permit us to decide new languages? Theorem (Space Hierarchy Theorem): For every proper complexity function f(n) ≥ log n: SPACE(f(n)) ( SPACE(f(n) log f(n)). Proof: same ideas. April 3, 201522 Robust Time and Space Classes What is meant by “robust/

##### 1 Week5 – Schema Why Schema? Schemas vs. DTDs Introduction – W3C vs. Microsoft XDR Schema, How To? Element Types – Simple vs. Complex Attributes Restrictions/Facets.

of characters that are acceptable totalDigits Specifies the exact number of digits allowed. Must be greater than zero whiteSpace Specifies how white space (line feeds, tabs, spaces, and carriage returns) is handled 33 XML Data Types (cont.) 34 Elements – Complex (cont.) What is a Complex Element? –A complex element is an XML element that contains other elements and/or attributes. –There are four kinds of/

##### Mind from brain: psychological spaces and neuroscience. Włodzisław Duch Department of Computer Methods, Nicholas Copernicus University, Toruń, Poland.

A=B+C, A=B×C, A  1 =B  1 +C  1, have identical geometric interpretation! 13 True, 14 False facts; simple P-space, complex neurodynamics. Geometric representation of facts: + increasing, 0 constant, - decreasing. Ohm’s law V=I×R; Kirhoff’s V=V 1 +V 2. True (I/, A=B×C, A  1 =B  1 +C  1, have identical geometric interpretation! 13 True, 14 False facts; simple P-space, complex neurodynamics. Question in qualitative physics: if R 2 increases, R 1 and V t are constant, what happens with current and V 1, V 2/

##### 1 Hybrid of search and inference: time- space tradeoffs chapter 10 ICS-275A Fall 2003.

), if elim-cond(b) is applied along ordering d when Y is a b-cutset then the space complexity of elim-cond(b) is O(n exp(b)), and its time complexity is O(n exp (|Y|+b)). Fall 2003 ICS 275A - Constraint Networks 19 Finding a b/For b=1, hybrid(1,1) is the non-separable components utilizing the cycle-cutset in each component. The space complexity of this algorithm is linear but its time complexity can be much better than the cycle-cutsets cheme or the non-separable component approach alone. Fall 2003 ICS 275A /

##### CS151 Complexity Theory Lecture 2 April 1, 2004. CS151 Lecture 22 Time and Space A motivating question: –Boolean formula with n nodes –evaluate using.

all n –there exists a TM M that outputs exactly f(n) symbols on input 1 n, and runs in time O(f(n) + n) and space O(f(n)). April 1, 2004CS151 Lecture 220 Proper Complexity Functions includes all reasonable functions we will work with –log n, √n, n 2, 2 n, n!, … –if f and g are proper then f/

##### 1.Understanding Systems Roberto Poli 1. My short course  Understanding Systems  What is a System?  Structure and Function  Complicated vs. Complex.

Morris, 2008)  When searching for a solution to its problems, life apparently does not traverse the entire combinatorial space of possibilities, but continues to discover the same solutions which suggest that optimality criteria (or variational principles) are at/, intelligence and anticipation  What else is needed, apart from variation and selection? 28 Two types of complexity Complexity 1 29 Simple vs. complex 1 systems  Single cause and single effect (one-to-one connection)  Small changes in the cause/

##### Advanced Information Architecture- Fall 02 The sociotechnical analysis of complex web sites I. Introducing information architecture II. The roots of IA:

rigor to IA research Usability, experimentation, ethnography Dealing with ambiguity and complexity is also intuitive Advanced Information Architecture- Fall 02 It focuses on digital (web-based) information spaces A set of items held by an information system and the relations /http://www.ils.unc.edu/gbnewby/papers/building4.html http://www.ils.unc.edu/gbnewby/papers/building4.html A complex information space (C) stores a total number (N) of information units in a medium (M) of storage A user (X) /

##### Los Angeles Palo Alto © 2004 Accelerating.org John Smart Space Frontier Conference 2004 (accelerating.org/slides.html) Exploring Micro and Macro Frontiers:

types of technological systems that are progressively able to do more for us, in a more networked and resilient fashion, using less resources (matter, energy, space, time, human and economic capital) to deliver any fixed amount of complexity, productivity, or capability. We are faced daily with many possible evolutionary choices in which to invest our precious time, energy, and resources, but only/

##### Soloviev Vladimir Alexeyevich – First Deputy of General Designer at S.P. Korolev Rocket and Space Corporation Energia, the Roscosmos’s STAC Chair Research.

involvement of additional resources and means into the research process directly during spaceflight is provided Crew member’s role in space programs implementation 9 Some examples of crewmembers’ function uniqueness aboard human space complexes Mir ISS Aboard Mir orbiting complex 5 research facilities of Priroda hardware complex were repaired, aboard the ISS RS – the Laser communication system, instruments for crew Earth observation, etc.; during the/

##### An Experimental Study on the Effects of Wake Interference on the Performance of Wind Turbines over Flat and Complex Terrains Advanced Flow Diagnostics.

wind turbine sited on flat surface ) 0.901.910.67 2.13 2.130.91 SUMMARY Factors affecting the complex dynamics of the wind farms were investigated in detail; Factors affecting the complex dynamics of the wind farms were investigated in detail; Turbine spacing Turbine spacing Wind farm layout (aligned and staggered) Wind farm layout (aligned and staggered) Upstream turbine operating (yaw) conditions Upstream/

##### Space Partitioning Computer Graphics. What is Space Partitioning? A division of 3D space into distinct regions Specifically, a tree data structure is.

How many object are in the scene and how they are distributed How complex each particular object is –Check out gametutorials Frustum culling tutorial Octrees Octrees are a space partitioning data structure –We saw Octrees before in the context of modeling / m is the number of triangles per object –So it becomes infeasible as scene complexity or object complexity increases Collision Detection The solution is two-fold: –Space Partitioning Reduces the n 2 term –Bounding Volumes Reduces the m 2 term Collision /

##### Высокоэллиптическая гидрометеорологическая космическая система «Арктика» State Centre on Space Hydrometeorology "Planeta" Lavochkin Association 1 High-elliptical.

” and “Spectr-R” spacecrafts models, production of models of the new designed onboard instruments and units of the spacecrafts. Development of the work documentation on the equipment of Ground Control Complex and Ground Complex on the Data Receiving, Processing and Distribution of the Space Complexes “Electro-L” and “Spectr-R” Update of the existing onboard and ground hardware and software for the “Arctica/

##### Bell Laboratories Data Complexity Analysis: Linkage between Context and Solution in Classification Tin Kam Ho With contributions from Mitra Basu, Ester.

of Competence by NN and LP Best Classifier for Benchmarking Data All Rights Reserved © Alcatel-Lucent 2008 22 Regions in complexity space where the best classifier is (nn,lp, or odt) vs. an ensemble technique Boundary-NonLinNN IntraInter-Pretop MaxEff-/-crossing edges randomly [Macia et al. 2008] or, create partitions with increasing resolution can create continuous cover of complexity space but, are the data similar to those arising from reality? All Rights Reserved © Alcatel-Lucent 2008 29 Ways/

##### Algebra Jeff Edmonds York University COSC 6111 Fields GCD Powers mod p Fermat, Roots of Unity, & Generators Z mod p vs Complex Numbers Cryptography Other.

Fields GCD Powers mod p Fermat, Roots of Unity, & Generators Z mod p vs Complex Numbers Cryptography Other Finite Fields Vector Spaces Colour Error Correcting Codes Linear Transformations Integrating Changing Basis Fourier Transformation (sine) Fourier Transformation /b a×b=1, i.e. b=a -1 Examples: Reals & Rationals Complex Numbers Integers Invertible Matrices ( & a×0 = 0) Fields Problems for computers: Reals Too much space Lack of precision Integers Lack of inverses Grow too big Better field? Finite field, /

##### 91.102 - Computing II Lists(more complex than before…) List Representations Generalized Lists (and Lists of Lists...) Strings C strings Pascal strings.

one can maintain a “current pointer” and do searches both forwards and backwards along the list. Disadvantages: extra complexity in the data structures; more space used, especially if the Items are small. int Delete(ItemType *X, ListNode **L, int pos) { / Master Pointers...... Heap After Compaction 91.102 - Computing II All of these methods are complex, and all of them involve various time-space-complexity trade-offs. Unfortunately, the moment we moved away from the single-task personal computer (once/

##### JASS 2005 Saint Petersburg Space-Filling Curves An Introduction Presented by Levi Valgaerts.

a 2D computational grid... Favorable property: better exploitation of the 2D locality due to the recursive nature / self-similarity. Application of space-filling curves JASS 2005 Saint Petersburg Application of space-filling curves 1. Representation of computational grids (1) Acceptable computational complexity is required in implemen- ting computational grids. Especially for adaptively refined grids the manipulation part cannot be too expensive  choice of/

##### On the union of cylinders in 3-space Esther Ezra Duke University.

of any cylinder). Input: S = {S 1, …, S n } a collection of n simply-shaped bodies in d -space of constant description complexity. The problem: What is the maximal number of vertices/edges/faces that form the boundary of the union of the bodies in S/{F  F} F(x), for x  R 2. The complexity envelopes [Sharir 1994] The combinatorial complexity of the lower envelope of n simple algebraic surfaces in d -space is O*(n d-1 ). For d=3, the complexity of the lower envelope: O*(n 2 ) The sandwich region [ Agarwal/

##### Autonomous Large Distributed CubeSat Space Telescope (ALDCST) ASTE 527: Space Exploration Architectures Concepts Synthesis Studio Midterm Presentation.

/gnclab/Conference.html http://www.nps.edu/academics/gnclab/Conference.html 18 Thank you for your time! Jesus Isarraras isarrara@usc.edu 19 BACKUP CHARTS 20 CONCEPT - COMPLEX SUBSYSTEMS Large Space Aperture Architecture Comparison ALDCSTHSTJWST Herschel Space Observatory Type of MirrorSegmentedMonolithicSegmentedMonolithic Primary Aperture (m) 202.4 / 0.36.53.5 Mirror Mass (kg) 635 (mirrors, actuators) 828705300 (full telescope) Wavelength ( μm).11 - 2/

##### Outline for 4/2 Introduction & Logistics Notion of a Problem Space Search Techniques Video: Kasparov vs. Deep Blue Constraint Satisfaction Techniques.

-optimal step –Reduce probability(non-optimal) over time Comparison to Hill Climbing –Completeness? –Speed? –Space Complexity? temp Limited Discrepancy Search Discrepancy bound indicates how often to violate heuristic Iteratively increase... a b c/ search with admissible heuristic –Plus keep checking until all possibilities look worse Evaluation –Finds optimal solution? –Time Complexity? –Space Complexity? Yes O(b^d) Underestimates cost of any solution which can reached from node Admissable Heuristics f(x)/

##### THE PARADIGM OF COMPLEX SYSTEMS M.G.Mahjani K.N.Toosi University of Technology

on in the system.  The most remarkable feature to be stressed in the sudden transition from simple to complex behavior is the order and coherence of this system. This suggest the existence of correlations that is statistically. Long Range Correlation  The characteristic space dimension of Benard cell in usual laboratory conditions is in the order 10 -1 cm the whereas the characteristic/

##### Algorithm Analysis 1 Problem Solving Space Complexity Time Complexity Classifying Functions by Their Asymptotic Growth.

bugs, ensure compatibility across different versions  Maintenance 5 3. Algorithm Analysis Space complexity How much space is required Time complexity How much time does it take to run the algorithm 6 Space Complexity Space complexity = The amount of memory required by an algorithm to run to completion/ e.g. actual text - load 2GB of text VS. load 1MB of text 8 Time Complexity Often more important than space complexity space available tends to be larger and larger time is still a problem for all of us 3-4GHz/

##### Ontologies Reasoning Components Agents Simulations Agents Solving Problems by Environment State Space Search Jacques Robin.

nodes  With such test  Depth-first, backtracking and iterative deepening search loose their linear worst- case space complexity,  for any guarantee to avoid all loops may require keeping an exponential number of expanded nodes in / search algorithms do not scale up,  neither theoretically (exponential worst case time or space complexity)  nor empirically (experimentally measured average case time or space complexity)  Heuristic search algorithms do scale up to very large problem instances, in some /