Given a set of point P in Rd, a clustering problem is to partition P into k subsets {P1, P2, · · · , Pk} in such a way that a given objective function is minimized. The most studied cost functions for a cluster, μ(Pi), are maximum or average radius of Pi, maximum diameter of Pi, and maximum width of Pi. The overall objective function is ⊕ μ(Pi), where ⊕ is typically the Lp-norm operator. The mo...

A finite set A of integers is square-sum-free if there is no subset of A sums up to a square. In 1986, Erdős posed the problem of determining the largest cardinality of a square-sum-free subset of {1, . . . , n}. Answering this question, we show that this maximum cardinality is of order n1/3+o(1).

The capacity region of the N -sender additive white Gaussian noise (AWGN) multiple access channel (MAC) with feedback is not known in general, despite significant contributions by Cover, Leung, Ozarow, Thomas, Pombra, Ordentlich, Kramer, and Gastpar. This paper studies the class of generalized linear feedback codes that includes (nonlinear) nonfeedback codes at one extreme and the linear feedba...

In a wireless transmission network, relay node or intermediate nodes play a very important role. Thus, the use of relay transmission offers significant performance benefits, including being able to achieve spatial diversity through node cooperation and extending coverage without requiring large transmitter powers. In this paper, we consider a Physical-layer Network Coding (PNC) scheme for a two...

Interference alignment is known to achieve the maximum sum DoF of 4M 3 in the 2 × 2 X-Network (i.e., twotransmitter (Tx) two-receiver (Rx) X-Network) with M antennas at each node, as demonstrated by Jafar and Shamai. Recently, an Alamouti code based transmission scheme, which we call the Li-Jafarkhani-Jafar (LJJ) scheme, was proposed for the 2×2 XNetwork with two antennas at each node. This sch...

The importance of zinc for human health has been recognized since the early 1960s, but today there is little concern about zinc deficiency in developed countries. In this study, we measured the zinc concentration in hair from 28,424 Japanese subjects (18,812 females and 9,612 males) and found that 1,754 subjects (6.17%) had zinc concentrations lower than 2 standard deviations (86.3 ppm) below t...

In this work, we obtain the following new results: – Given a tree T = (V, E) with a length function ` : E → R and a weight function w : E → R, a positive integer k, and an interval [L, U ], the Weight-Constrained k Longest Paths problem is to find the k longest paths among all paths in T with weights in the interval [L,U ]. We show that the Weight-Constrained k Longest Paths problem has a lower...

The problem of minimum color sum of a graph is to color the vertices of the graph such that the sum (average) of all assigned colors is minimum. Recently, in [BBH+96], it was shown that in general graphs this problem cannot be approximated within n1 , for any > 0, unless NP = ZPP . In the same paper, a 9=8-approximation algorithm was presented for bipartite graphs. The hardness question for thi...

Given a sequence of n real numbers A = a1, a2, . . . , an and a positive integer k, the Sum Selection Problem is to find the segment A(i, j) = ai, ai+1, . . . , aj such that the rank of the sum s(i, j) = j t=i at is k over all n(n−1) 2 segments. We present a deterministic algorithm for this problem that runs in O(n log n) time. The previously best known randomized algorithm for this problem run...

An experimental evaluation of Bagging K-nearest neighbor classifiers (KNN) is performed. The goal is to investigate whether varying soft methods of aggregation would yield better results than Sum and Vote. We evaluate the performance of Sum, Product, MProduct, Minimum, Maximum, Median and Vote under varying parameters. The results over different training set sizes show minor improvement due to ...