An Introduction to Online Computation: Determinism, Randomization

In this review of An Introduction to Online Computation: Determinism, Randomization, Advice, the bottom line is clear: this textbook is a targeted, rigorous introduction to online algorithms and the emerging area of advice complexity for students and researchers. It assumes basic algorithmics and discrete mathematics, and the strongest reason to choose it is its focused treatment of both classical online problems and the role of randomness and advice, making it a practical reference for coursework or research reading lists.

Key Features

• Comprehensive coverage: Presents core topics in online computation, giving readers a coherent path from basics to advanced models including advice and randomization.
• Problem-driven approach: Analyzes canonical problems like paging, the k-server problem, and knapsack to show how techniques apply across settings.
• Theoretical depth: Explains the formal frameworks behind determinism and randomization so students can follow proofs and complexity arguments.
• Advice complexity focus: Introduces advice as a formal resource and surveys recent results, useful for researchers exploring this newer direction.
• Suitable for courses: Written at a level appropriate for undergraduates and graduates with basic discrete math and algorithm knowledge, enabling adoption in classes.

Who It's For

Students in upper-level undergraduate or graduate computer science courses who have already covered algorithm design and discrete mathematics will find this text most useful; it gives a clear theoretical foundation and worked examples from common online problems. Instructors building a course module on online algorithms or advice complexity can rely on its structured presentation and problem selection.

Researchers seeking a compact reference on advice complexity and randomized online algorithms will also appreciate the focused survey and citations. Readers without a background in algorithms or discrete math, or those looking for primarily empirical or implementation-focused content, should look elsewhere for gentler introductions.

Pros & Cons

Pros

• Consolidates multiple online computation models, helping readers compare determinism, randomization, and advice in one place.
• Uses classical problems like paging and k-server to illustrate techniques, which aids comprehension through examples.
• Balances student-level exposition with material that is valuable for researchers as a reference.

Cons

• Not intended as a beginner's primer; requires prior algorithmic and discrete math knowledge.

Specifications

Title	An Introduction to Online Computation: Determinism, Randomization, Advice
Series	Texts in Theoretical Computer Science. An EATCS Series
Author	Dennis Komm
Audience	Undergraduate and graduate computer science students, researchers
Main topics	Online computation, randomization, advice complexity, paging, k-server, scheduling, knapsack
Use cases	Course textbook, research reference

Our Verdict

An Introduction to Online Computation is a well-focused textbook that delivers theoretical clarity on determinism, randomization, and advice complexity using standard online problems as illustrations. Students who already know basic algorithmics and discrete mathematics will find it excellent course material, and researchers will value its concise survey of advice complexity, making it worthwhile for academic use and reference.

Frequently Asked Questions

Is this book suitable for beginners?
It assumes basic knowledge in algorithmics and discrete mathematics, so beginners should first build that foundation before using this book.

Does it cover practical implementations?
The focus is theoretical analysis of online problems and advice complexity rather than implementation details or empirical evaluation.

Which problems are discussed?
The book analyzes problems such as paging, the k-server problem, job shop scheduling, knapsack, and bit guessing, among others.