We present a new way to encode weighted sums into unweighted pairwise constraints, obtaining the following results. – Define the k-SUM problem to be: given n integers in [−n, n] are there k which sum to zero? (It is well known that the same problem over arbitrary integers is equivalent to the above definition, by linear-time randomized reductions.) We prove that this definition of k-SUM remains...

The technological development of Internet Things (IoT) applications is emerging and attracting the attention real world in automated industry, agriculture, environment, scientific community. In most scenarios, extending network lifetime an IoT highly challenging because constrained nodes. wireless sensor (WSN) core component applications. addition, WSN nodes are required for processes, particul...

A weighted automaton is functional if any two accepting runs on the same finite word have the same value. In this paper, we investigate functional weighted automata for four different measures: the sum, the mean, the discounted sum of weights along edges and the ratio between rewards and costs. On the positive side, we show that functionality is decidable for the four measures. Furthermore, the...

Inverse maximum flow (IMDF), is among the most important problems in the field ofdynamic network flow, which has been considered the Euclidean norms measure in previousresearches. However, recent studies have mainly focused on the inverse problems under theHamming distance measure due to their practical and important applications. In this paper,we studies a general approach for handling the inv...

A continuous time mean-variance (MV) problem optimizes the bi-objective criteria 5 (V, E), respectively representing variance V and expected value E of a random variable at the end 6 of a time horizon T . This problem is computationally challenging since the dynamic programming 7 principle cannot be directly applied to the variance criterion. An embedding technique has been 8 proposed in [18, 2...