How Long to Read Hamiltonian Cycle Problem and Markov Chains

How Long Does it Take to Read Hamiltonian Cycle Problem and Markov Chains?

It takes the average reader 3 hours and 23 minutes to read Hamiltonian Cycle Problem and Markov Chains by Vivek S. Borkar

Assuming a reading speed of 250 words per minute. Learn more

Description

This research monograph summarizes a line of research that maps certain classical problems of discrete mathematics and operations research - such as the Hamiltonian Cycle and the Travelling Salesman Problems - into convex domains where continuum analysis can be carried out. Arguably, the inherent difficulty of these, now classical, problems stems precisely from the discrete nature of domains in which these problems are posed. The convexification of domains underpinning these results is achieved by assigning probabilistic interpretation to key elements of the original deterministic problems. In particular, the approaches summarized here build on a technique that embeds Hamiltonian Cycle and Travelling Salesman Problems in a structured singularly perturbed Markov decision process. The unifying idea is to interpret subgraphs traced out by deterministic policies (including Hamiltonian cycles, if any) as extreme points of a convex polyhedron in a space filled with randomized policies. The above innovative approach has now evolved to the point where there are many, both theoretical and algorithmic, results that exploit the nexus between graph theoretic structures and both probabilistic and algebraic entities of related Markov chains. The latter include moments of first return times, limiting frequencies of visits to nodes, or the spectra of certain matrices traditionally associated with the analysis of Markov chains. However, these results and algorithms are dispersed over many research papers appearing in journals catering to disparate audiences. As a result, the published manuscripts are often written in a very terse manner and use disparate notation, thereby making it difficult for new researchers to make use of the many reported advances. Hence the main purpose of this book is to present a concise and yet easily accessible synthesis of the majority of the theoretical and algorithmic results obtained so far. In addition, the book discusses numerous open questions and problems that arise from this body of work and which are yet to be fully solved. The approach casts the Hamiltonian Cycle Problem in a mathematical framework that permits analytical concepts and techniques, not used hitherto in this context, to be brought to bear to further clarify both the underlying difficulty of NP-completeness of this problem and the relative exceptionality of truly difficult instances. Finally, the material is arranged in such a manner that the introductory chapters require very little mathematical background and discuss instances of graphs with interesting structures that motivated a lot of the research in this topic. More difficult results are introduced later and are illustrated with numerous examples.

How long is Hamiltonian Cycle Problem and Markov Chains?

Hamiltonian Cycle Problem and Markov Chains by Vivek S. Borkar is 202 pages long, and a total of 50,904 words.

This makes it 68% the length of the average book. It also has 62% more words than the average book.

How Long Does it Take to Read Hamiltonian Cycle Problem and Markov Chains Aloud?

The average oral reading speed is 183 words per minute. This means it takes 4 hours and 38 minutes to read Hamiltonian Cycle Problem and Markov Chains aloud.

What Reading Level is Hamiltonian Cycle Problem and Markov Chains?

Hamiltonian Cycle Problem and Markov Chains is suitable for students ages 12 and up.

Note that there may be other factors that effect this rating besides length that are not factored in on this page. This may include things like complex language or sensitive topics not suitable for students of certain ages.

When deciding what to show young students always use your best judgement and consult a professional.

Where Can I Buy Hamiltonian Cycle Problem and Markov Chains?

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