text: By using different interface adapters for different methods, it is possible to construct a maximally covering web of interface adapters which incurs minimum loss during interface adaptation. We introduce a polynomial-time algorithm that can achieve this. However, we also show that minimizing the number of adapters included in a maximally covering web of interface adapters is an NP-complete problem.
  @cite_3: Despite providing similar functionality, multiple network services may require the use of different interfaces to access the functionality, and this problem will only become worse with the widespread deployment of ubiquitous computing environments. One way around this problem is to use interface adapters that adapt one interface into another. Chaining these adapters allows flexible interface adaptation with fewer adapters, but the loss incurred because of imperfect interface adaptation must be considered. This study outlines a matrix-based mathematical basis for analysing the chaining of lossy interface adapters. The authors also show that the problem of finding an optimal interface adapter chain is NP-complete with a reduction from 3SAT.
  @cite_2: A key feature of ubiquitous computing is service continuity which allows a user to transparently continue his task regardless of his movement. For service continuity, the underlying system needs to not only discover a service satisfying a user's request, but also provide an interface differences resolution scheme if the interface of the service found is not the same as that of the service requested. For resolving interface mismatches, one of solutions is to use an interface adapter. The most serious problem in the interface adapter-based approach is the overhead of adapter generation. There are many research efforts about adapter generation load reduction and this paper focuses on an adapter chaining scheme to reduce the number of necessary adapters among different service interfaces. We propose a construction-time adaptation loss evaluation scheme and an adapter chain construction algorithm, which finds an adapter chain with minimal adaptation loss.
summary: @cite_2 proposes an interface adaptation framework which attempts to minimize the loss incurred by an interface adapter chain, and @cite_3 rigorously defines the mathematical background required to implement such a framework. These only consider the use of single chains of interface adapters.