We show that every language in NP has a probablistic verifier that checks membership
proofs for it using logarithmic number of random bits and by examining a constant number of …

Algorithmic design, especially for hard problems, is more essential for success in solving
them than any standard improvement of current computer tech nologies. Because of this, the …

Graph-based modeling has emerged as a powerful abstraction capable of capturing in a
single and unified framework many of the relational, spatial, topological, and other …

We consider the problem of coloring k-colorable graphs with the fewest possible colors. We
present a randomized polynomial time algorithm that colors a 3-colorable graph on n …

The minimum- degree Greedy algorithm, or Greedy for short, is one of the~ implest, most
efficient, and most thoroughly studied methods for finding independent sets in graphs. We …

We survey approximation algorithms for some well-known and very natural combinatorial
optimization problems, the minimum set covering, the minimum vertex covering, the …

Reactive Search integrates sub-symbolic machine learning techniques into search
heuristics for solving complex optimization problems. By automatically adjusting the working …

Due to the fact that no NP-complete problem can be solved in polynomial time (unless P=
NP), many approximability results (both positive and negative) of NP-hard optimization …

We present a linear programming-based method for finding" gadgets," ie, combinatorial
structures reducing constraints of one optimization problem to constraints of another. A key …

Result diversification is an important aspect in web-based search, document summarization,
facility location, portfolio management, and other applications. Given a set of ranked results …