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The classical distinction between polynomial time solvable and NP-hard problems is often too coarse. This course covers techniques for proving more fine-grained lower and upper bounds on complexity of
The knapsack problem is the following problem in combinatorial optimization: Given a set of items, each with a weight and a value, determine which items to include in the collection so that the total weight is less than or equal to a given limit and the total value is as large as possible. It derives its name from the problem faced by someone who is constrained by a fixed-size knapsack and must fill it with the most valuable items.
Problem solving is the process of achieving a goal by overcoming obstacles, a frequent part of most activities. Problems in need of solutions range from simple personal tasks (e.g. how to turn on an appliance) to complex issues in business and technical fields. The former is an example of simple problem solving (SPS) addressing one issue, whereas the latter is complex problem solving (CPS) with multiple interrelated obstacles.
Effective caching is crucial for performance of modern-day computing systems. A key optimization problem arising in caching – which item to evict to make room for a new item – cannot be optimally solv
We study the basic problem of assigning memoryless workers to tasks with dynamically changing demands. Given a set of w workers and a multiset T ⊆ [t] of |T| = w tasks, a memoryless worker-task assign
Schloss Dagstuhl -- Leibniz-Zentrum fur Informatik2022
We solve the Bin Packing problem in O^*(2^k) time, where k is the number of items less or equal to one third of the bin capacity. This parameter measures the distance from the polynomially solvable ca
Schloss Dagstuhl – Leibniz-Zentrum fur Informatik2022