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2 edition of On the complexity of the st-connectivity problem found in the catalog.

On the complexity of the st-connectivity problem

Chung Keung Poon

# On the complexity of the st-connectivity problem

## by Chung Keung Poon

Published by University of Toronto, Dept. of Computer Science in Toronto .
Written in English

Edition Notes

Thesis (Ph.D.)--University of Toronto, 1996.

The Physical Object ID Numbers Statement Chung Keung Poon. Pagination 92 p. Number of Pages 92 Open Library OL17373412M ISBN 10 0612118312

There is more and more growing interest in the design of efficient (graph) exploration methods The motivation is very broad and it comes from Robotics algorithmic agent design industry (e.g., vacuum cleaners) Computational complexity st-connectivity problem and related classes of problems Biologically motivated computing understanding behaviour. Thanks for contributing an answer to Computer Science Stack Exchange! Please be sure to answer the question. Provide details and share your research! But avoid Asking for help, clarification, or responding to other answers. Making statements based on opinion; back them up with references or personal experience. Use MathJax to format equations.

time [ 82, ]. The fastest known classical algorithm for integer factorization is the general number field sieve, which is believed to run in time. 2 O ~ (n 1 / 3). The best rigorously proven upper bound on the classical complexity of factoring is. O (2 n / 4 + o (1)) via the Pollard-Strassen algorithm [ , ]. Shor's factoring. Problem reduction and proof technique for undecidability. Halting problem Talk by Faisal on virtual currency 05 09 Febru More examples of undecidable problems from Sipser's book By Javeria on properties of quantum particles Regular languages' space .

On the Complexity of the G-Reconstruction Problem. Pages Simulating Undirected st-Connectivity Algorithms on Uniform JAGs and NNJAGs. Pages Book Title Algorithms and Computation Book Subtitle 16th International Symposium, ISAAC , Sanya, Hainan, China, December , , Proceedings. Reingold's proof showing that UNDIRECTED-ST-CONNECTIVITY is in L. Communication complexity: See the book by Nisan and Kushilevitz for background material. Information theory methods in communication complexity D. Sivakumar, Ziv Bar-Yossef, T.S. Jayram and S. Ravi Kumar.

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### On the complexity of the st-connectivity problem by Chung Keung Poon Download PDF EPUB FB2

In computer science, st-connectivity or STCON is a decision problem asking, for vertices s and t in a directed graph, if t is reachable from s. Formally, the decision problem is given by PATH = { D, s, t | D is a directed graph with a path from vertex s to t}. Complexity. The problem can be shown to be in NL, as a non-deterministic Turing machine can guess the next node of the path, while the.

Chapter of Wigderson's book: The class coNP, the NP versus coNP question, and efficient characterization Chapter 6 of Wigderson's book: Proof complexity Propositional proof complexity: past, present, and future, Paul Beame and Toniann Pitassi The limits of proof, video of a talk by Paul Beame Proof complexityvideo of a talk by Paul Beame.

Every monotone circuit for CONN has size $\Omega(n^3)$: CONN has almost the same monotone complexity as boolean multiplication of two boolean matrices, and this latter problem is shown, by Paterson () and by Mehlhorn-Galil (), to require $\Omega(n^3)$ gates. Abstract. In Membrane Computing, the solution of a decision problem $$X$$ belonging to the complexity class P via a polynomially uniform family of recognizer P systems is trivial, since the polynomial encoding of the input can involve the solution of the problem.

The design of such solution has one membrane, two objects, two rules and one computation by: 2. from book Approximation, G with query complexity q = (2 / The main idea of the proo f is to reduce the problem of testing st-connectivity in the orien tation model to the.

On the complexity of the st-connectivity problem Chung Keung Poon Doctor of Philosophy Department of Computer Science University of Toronto The directed st-connectivity problem is Author: Usha Satish.

Chapters and 6 of Wigderson's book Gödel's letter to von Neumann Propositional proof complexity: past, present, and future, Paul Beame and Toniann. One important NL-complete problem is ST-connectivity (or "Reachability") (Papadimitriou Thrm. ), the problem of determining whether, given a directed graph G and two nodes s and t on that graph, there is a path from s to t.

Directed st-connectivity is the problem of deciding whether or not there exists a path from a distinguished node s to a distinguished node t in a directed graph. We prove a time--space lower bound on the probabilistic NNJAG model of Poon [Proc.

34th Annual Symposium on Foundations of Computer Science, Palo Alto, CA,pp. ].Let n be the number of nodes in the input graph and S and Cited by: Abstract. In a breakthrough result, Reingold [17] showed that the Undirected st-Connectivity problem can be solved in O(log n) next major challenge in this direction is whether one can extend it to directed graphs, and thereby lowering the deterministic space complexity of $$\mathcal{RL}$$ or $$\mathcal{NL}$$.In this paper, we show that Reingold’s algorithm, the O(log 4/3 n)-space Cited by: 8.

Directed st-connectivity is the problem of deciding whether or not there exists a path from a distinguished node s to a distinguished node t in a directed graph.

We prove a time--space lower bound Cited by: There are two related complexity classes in $\text{NL}$ which are also in $\text{LogDCFL}$, which puts them in $\text{SC}^2$ (by Cook).

The first is $\text{RUL}$, for "Reach-Unambiguous Log-space" which has reachability in mangroves (graphs where every pair of vertices has at most one directed path between them) as a complete problem. We improve this algorithm for the special case when the network is planar, meaning no two edges of the network cross each other.

We show that to evaluate a formula, it is sufficient to solve a related st-connectivity problem on a planar network, and so our new st-connectivity algorithm can also be used to evaluate by: 1. This is a very important problem to understand the algorithmic and structural differences between undirected and directed width parameters.

Space complexity: Is Planar ST-connectvity in logspace. This is perhaps the most natural special case of the NL vs L problem. Planar ST-connectivity is known to be in. Recently, Imai, Nakagawa, Pavan.

The papers in this book stem from the London Mathematical Society Symposium on Boolean Function Complexity held at Durham University in July The range of topics covered will be of interest to the newcomer to the field as well as the expert, and overall the papers are representative of the research presented at the Symposium.

Within this new setting, Communication Complexity gives simpler proofs to old results and demonstrates the usefulness of the approach by presenting a depth lower bound for st-connectivity. Karchmer concludes by proposing open problems which point toward proving a general depth lower by: Get this from a library.

Algorithms-- ESA 20th Annual European Symposium, Ljubljana, Slovenia, SeptemberProceedings. [Leah Epstein; Paolo Ferragina;] -- This book constitutes the refereed proceedings of the 20th Annual European Symposium on Algorithms, ESAheld in Ljubljana, Slovenia, in September in the context of the combined conference.

In this way, we demonstrate the complexity class P is not equal to NP by the reduction ad absurdum rule. Another major complexity classes are LOGSPACE and NLOGSPACE. Whether LOGSPACE = NLOGSPACE is another fundamental question that it is as important as it is unresolved.

We show the problem MAXIMUM can be solved in logarithmic space. Lecture 2: Friday, Febru NP completeness,CoNP, the Polynomial Hierarchy and P/poly Lecture outline. Reading: Chapter 2,5,6. Additional reading: My philosophical musings are not original and largely based on what I believe to be the best survey ever written on complexity: A Personal View of Average Complexity by Russell Impagliazzo.

One way to phrase complexity theory's mission is. In computer science and computational complexity theory, st-connectivity or STCON is a decision problem asking, for vertices s and t in a directed graph, if t is reachable from s. Formally, the decision problem is given by.

New!!: P (complexity) and St-connectivity See more» Thomas H. Cormen. We will follow the book by Sanjeev Arora and Boaz Barak, and will try to cover part 1 of it.

I may add/delete some topics as we go on. Reference books. Computational Complexity: A Modern Approach by Sanjeev Arora, and Boaz Barak Online draft[AB] Computational Complexity by .Stack Exchange network consists of Q&A communities including Stack Overflow, the largest, most trusted online community for developers to learn, share .NP-completeness of the Traveling Salesman Problem.

Further directions of computational complexity theory: average-case complexity, possible consequences of P=NP, existence of one-way and trapdoor functions.

Discussion of exercises; complexity of CLIQUE for constant clique size k; consequences of allowing exponential.