2 research outputs found
On Self-Reducibility and Reoptimization of Closest Substring Problem
In this paper, we define the reoptimization variant of the closest substring
problem (CSP) under sequence addition. We show that, even with the additional
information we have about the problem instance, the problem of finding a
closest substring is still NP-hard. We investigate the combinatorial property
of optimization problems called self-reducibility. We show that problems that
are polynomial-time reducible to self-reducible problems also exhibits the same
property. We illustrate this in the context of CSP. We used the property to
show that although we cannot improve the approximability of the problem, we can
improve the running time of the existing PTAS for CSP.Comment: 8 page
Aggregation of Composite Solutions: strategies, models, examples
The paper addresses aggregation issues for composite (modular) solutions. A
systemic view point is suggested for various aggregation problems. Several
solution structures are considered: sets, set morphologies, trees, etc. Mainly,
the aggregation approach is targeted to set morphologies. The aggregation
problems are based on basic structures as substructure, superstructure,
median/consensus, and extended median/consensus. In the last case, preliminary
structure is built (e.g., substructure, median/consensus) and addition of
solution elements is considered while taking into account profit of the
additional elements and total resource constraint. Four aggregation strategies
are examined: (i) extension strategy (designing a substructure of initial
solutions as "system kernel" and extension of the substructure by additional
elements); (ii) compression strategy (designing a superstructure of initial
solutions and deletion of some its elements); (iii) combined strategy; and (iv)
new design strategy to build a new solution over an extended domain of solution
elements. Numerical real-world examples (e.g., telemetry system, communication
protocol, student plan, security system, Web-based information system,
investment, educational courses) illustrate the suggested aggregation approach.Comment: 72 pages, 116 figures, 35 table