Our goal is to show tight bounds on the running time of algorithms for scheduling and
packing problems. To prove lower bounds, we investigate implications of the exponential …

We consider the classical scheduling problem on parallel identical machines to minimize the
makespan. There is a long history of studies on this problem, focusing on exact and …

We consider the classical scheduling problem on parallel identical machines to minimize the
makespan. There is a long history of study on this problem, focusing on exact and …

We present an algorithm to solve the subset‐sum problem (SSP) of capacity c and n items
with weights wi, 1≤ i≤ n, spending O (n (m− wmin)/p) time and O (n+ m− wmin) space in the …

This paper presents simple algorithms for 0/1 Knapsack and Bin Packing with a fixed
number of bins that achieve time complexity p n⋅ 2O x where x is the total bit length …

After a series of publications of TE O'Neil et al.(eg in 2010), dynamic programming seems to
be the most promising way to solve knapsack problems. Some techniques are known to …

This article describes several properties of the random problem space for the Subset Sum
problem, derived both empirically and analytically. Empirical results support the conjecture …

Abstract The Subset Sum problem is a well-known NP-complete problem. It can be
described as follows: given a set of positive integers S and a target sum t, is there a subset of …

Optimization has been a central topic in most scientific disciplines for centuries. Continuous
optimization has long benefited from well-established techniques of calculus. Discrete …

The research literature on NP-complete problems includes some attempts to identify easier
and harder problems within the class, and the results with respect to Subset Sum are not …