In this paper we extend recent work about the relationship between the syntactic description of NP optimization problems and their approximation properties. In contrast to Max SNP we consider problems that take arbitrary weighted structures as input instances and we use the framework of Metaanite Model Theory 5] to get a more general deenability theory of optimization problems. We deene a class...

We consider static-priority tasks with constraineddeadlines that are subjected to release jitters. We define an approximate worst-case response time analysis and we propose a polynomial time algorithm. For that purpose, we extend the Fully Polynomial Time Approximation Scheme (FPTAS) presented in [2] to take into account release jitters; this feasibility test is then used to define a polynomial...

In the knapsack problem, you are given a knapsack of size B ∈ Z and a set S = {a1, . . . , an} of objects with corresponding sizes and profits s(ai) ∈ Z and p(ai) ∈ Z. The goal is to find the optimal subset of objects whose total size is bounded by B and has the maximum possible total profit. This problem is also sometimes called the 0/1 knapsack problem because each object must be either in th...

We study flows over time in networks with transit times on the arcs. Transit times describe how long it takes to traverse an arc. A flow over time specifies for each arc a time-dependent flow rate that must always be bounded by the arc’s capacity. Only recently, Melkonian introduced an alternative model where so-called bridge capacities bound the total amount of flow traveling along an arc, at ...

Bargaining networks model social or economic situations in which agents seek to form the most lucrative partnership with another agent from among several alternatives. There has been a flurry of recent research studying Nash bargaining solutions (also called ‘balanced outcomes’) in bargaining networks, so that we now know when such solutions exist, and also that they can be computed efficiently...

An unconstrained nonlinear binary optimization problem of selecting a maximum expected value subset of items is considered. Each item is associated with a profit and probability. Each of the items succeeds or fails independently with the given probabilities, and the profit is obtained in the event that all selected items succeed. The objective is to select a subset that maximizes the total valu...

We consider computationally-efficient incentive-compatible mechanisms that use the VCG payment scheme, and study how well they can approximate the social welfare in auction settings. We obtain a 2-approximation for multi-unit auctions, and show that this is best possible, even though from a purely computational perspective an FPTAS exists. For combinatorial auctions among submodular (or subaddi...

We design a fully polynomial time approximation scheme (FPTAS) for counting the number of matchings (packings) in arbitrary 3-uniform hypergraphs of maximum degree three, referred to as (3, 3)hypergraphs. It is the first polynomial time approximation scheme for that problem, which includes also, as a special case, the 3D Matching counting problem for 3-partite (3, 3)-hypergraphs. The proof tech...

<p style='text-indent:20px;'>In this paper, we study the single-machine Pareto-scheduling of jobs with multiple weighting vectors for minimizing total weighted late works. Each vector has its corresponding work. The goal problem is to find Pareto-frontier works vectors. When number arbitrary, it implied in literature that unary NP-hard. Then concentrate on our research under assumption a ...