s : Our motivation is to answer some open problems in parallel scheduling problems. We consider problems that are NP-hard. A standard way of dealing with NP-hard problems is not to search for an optimal solution, but to go for near-optimal solutions in a polynomial time approximation algorithm. In this paper, we summarize what is known on minimizing schedule length or makespan criteria for para...

In this article we discuss the design of result verification algorithms for optimization problems. In particular, we design time-optimal result verification algorithms which verify the solution of all-pairs shortest paths, maximum flow, and matching problems. We prove that polynomial-time verification algorithms for AP-complete problems do not exist exist, unless P = NP. Result verification pro...

Bilevel programming, a tool for modeling decentralized decision problems, consists of the objective of the leader at its first level and that of the follower at the second level. Bilevel programming has been proved to be an Np-hard problem. Numerous algorithms have been developed for solving bilevel programming problems. These algorithms lack the required efficiency for solving a real problem. ...

Strong bisimilarity of Basic Parallel Processes (BPP) is decidable, but the best known algorithm has non-elementary complexity [7]. On the other hand, no lower bound for the problem was known. We show that strong bisimilarity of BPP is co-NP-hard. Weak bisimilarity of BPP is not known to be decidable, but an NP lower bound has been shown in [31]. We improve this result by showing that weak bisi...

Recently, due to the widespread diffusion of smart-phones, mobile puzzle games have experienced a huge increase in their popularity. A successful puzzle has to be both captivating and challenging, and it has been suggested that this features are somehow related to their computational complexity [5]. Indeed, many puzzle games – such as Mah-Jongg, Sokoban, Candy Crush, and 2048, to name a few – a...

Bilevel programming, a tool for modeling decentralized decision problems, consists of the objective of the leader at its first level and that of the follower at the second level. Bilevel programming has been proved to be an Np-hard problem. Numerous algorithms have been developed for solving bilevel programming problems. These algorithms lack the required efficiency for solving a real problem. ...