It is well-known that the multiple knapsack problem is NP-hard, and does not admit an FPTAS even for the case of two identical knapsacks. Whereas the 0-1 knapsack problem with only one knapsack has been intensively studied, and some effective exact or approximation algorithms exist. A natural approach for the multiple knapsack problem is to pack the knapsacks successively by using an effective ...

The Lead-Based Multiple Video Transmission (LMVT) problem is motivated by applications in managing the quality of experience (QoE) of video streaming for mobile clients. In an earlier work, the LMVT problem has been shown to be NP-hard for a specific bit-to-lead conversion function φ. In this work, we show the problem to be NP-hard even if the function φ is linear. We then design a fully polyno...

Counting the independent sets of a graph is classical #P-complete problem, even in bipartite case. We give an exponential-time approximation scheme for this problem which faster than best known algorithm exact problem. The running time our on general graphs with error tolerance ε at most O(20.2680n) times polynomial 1/ε. On graphs, exponential term improved to O(20.2372n). Our methods combine t...

Abstract We discuss a game theoretic variant of the subset sum problem, in which two players compete for common resource represented by knapsack. Each player owns private set items, pack items alternately, and each either wants to maximize total weight his own packed into knapsack or minimize other player. show that finding best packing strategy against hostile selfish adversary is PSPACE-compl...

We consider static-priority tasks with constraineddeadlines that are subjected to release jitter. We define an approximate worst-case response-time analysis and propose a polynomial-time algorithm. For that purpose, we extend the Fully Polynomial-Time Approximation Scheme (FPTAS) presented in [6] to take into account release jitter constraints; this feasibility test is then used to define a pol...

For a given node t in a directed graph G(VG, EG) and a positive integer k we study the problem of computing a set of k new links pointing to t – so called backlinks to t – producing the maximum increase in the PageRank value of t. This problem is known as Link Building in the www context. We present a theorem describing how the topology of the graph comes in to play when evaluating potential ne...

We give a fully polynomial-time approximation scheme (FPTAS) to count the number of q-colorings for k-uniform hypergraphs with maximum degree∆ if k ≥ 28 and q > 315∆ 14 k−14 . We also obtain a polynomial-time almost uniform sampler if q > 798∆ 16 k−16/3 . These are the first approximate counting and sampling algorithms in the regime q ≪ ∆ (for large ∆ and k) without any additional assumptions. ...

We consider a fundamental problem, called QoS-aware Multicommodity Flow, for assessing robustness in transportation planning. It constitutes a natural generalization of the weighted multicommodity ow problem, where the demands and commodity values are elastic to the Quality-of-Service (QoS) characteristics of the underlying network. The problem is also fundamental in other domains beyond transp...

In a recent paper [Discrete Appl. Math. 130 (2003) 449–467], Yang, Ye, and Zhang investigate the problem of scheduling independent jobs on two identical machines, with a limit on the number of jobs that can be assigned to each single machine, so as to minimize the total weighted completion time of the jobs. They provide a semidefinite programming based, polynomial time approximation algorithm w...

This paper presents the main results obtained in the field of approximation algorithms in a unified framework. Most of these results have been revisited in order to emphasize two basic tools useful for characterizing approximation classes, that is, combinatorial properties of problems and approximation preserving reducibilities. In particular, after reviewing the most important combinatorial ch...