On Computing Centroids According to the p-Norms of Hamming Distance Vectors

In this paper we consider the p-Norm Hamming Centroid problem which asks to determine whether some given strings have a centroid with a bound on the p-norm of its Hamming distances to the strings. Specifically, given a set S of strings and a real k, we consider the problem of determining whether there exists a string s^* with (sum_{s in S} d^{p}(s^*,s))^(1/p) <=k, where d(,) denotes the Hamming distance metric. This problem has important applications in data clustering and multi-winner committee elections, and is a generalization of the well-known polynomial-time solvable Consensus String (p=1) problem, as well as the NP-hard Closest String (p=infty) problem. Our main result shows that the problem is NP-hard for all fixed rational p > 1, closing the gap for all rational values of p between 1 and infty. Under standard complexity assumptions the reduction also implies that the problem has no 2^o(n+m)-time or 2^o(k^(p/(p+1)))-time algorithm, where m denotes the number of input strings and n denotes the length of each string, for any fixed p > 1. The first bound matches a straightforward brute-force algorithm. The second bound is tight in the sense that for each fixed epsilon > 0, we provide a 2^(k^(p/((p+1))+epsilon))-time algorithm. In the last part of the paper, we complement our hardness result by presenting a fixed-parameter algorithm and a factor-2 approximation algorithm for the problem

Services trade liberalization and regulatory reform : re-invigorating international cooperation

Trade and investment in services are inhibited by a range of policy restrictions, but the best offers so far in the Doha negotiations are on average twice as restrictive as actual policy. They will generate no additional market opening. Regulatory concerns help explain the limited progress. This paper develops two proposals to enhance the prospects for both liberalization of services trade and regulatory reform. The first is for governments to create mechanisms ("services knowledge platforms") to bring together regulators, trade officials, and stakeholders to discuss services regulatory reform. Such mechanisms could identify reform priorities and opportunities for utilization of"aid for trade"resources, thereby putting in place the preconditions for future market opening. The second proposal is for a new approach to negotiations in the World Trade Organization, with a critical mass of countries that account for the bulk of services production agreeing to lock-in applied levels of protection and pre-committing to reform of policies affecting foreign direct investment and international movement for individual service providers -- two areas where current policy is most restrictive and potential benefits from liberalization are greatest. If these proposals cannot be fully implemented in the Doha time frame, then any Doha agreement could at least lay the basis for a forward-looking program of international cooperation along the proposed lines.Trade and Services,Public Sector Corruption&Anticorruption Measures,Emerging Markets,Economic Theory&Research,ICT Policy and Strategies

Cost-optimal constrained correlation clustering via weighted partial Maximum Satisfiability

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