an injective map f : e(g) → {±1, ±2, · · · , ±q} is said to be an edge pair sum labeling of a graph g(p, q) if the induced vertex function f*: v (g) → z − {0} defined by f*(v) = (sigma e∈ev) f (e) is one-one, where ev denotes the set of edges in g that are incident with a vetex v and f*(v (g)) is either of the form {±k1, ±k2, · · · , ±kp/2} or {±k1, ±k2, · · · , ±k(p−1)/2} u {k(p+1)/2} accordin...

Recent results by Dinur et al. (2012) and Austrin et al. (2013) have improved the time-space tradeoff curve for SubsetSum. We analyze a family of hash functions previously introduced by Dietzfelbinger, and apply it to decompose arbitrary k-Sum instances into smaller ones. This allows us to extend the aforementioned tradeoff curve to the k-Sum problem, which is SubsetSum restricted to sets of si...

Secure Multiparty Computation (SMC) allows parties to know the result of cooperative computation while preserving privacy of individual data. Secure sum computation is an important application of SMC. In our proposed protocols parties are allowed to compute the sum while keeping their individual data secret with increased computation complexity for hacking individual data. In this paper the dat...

The k-SUM problem is given n input real numbers to determine whether any k of them sum to zero. The problem is of tremendous importance in the emerging field of complexity theory within P , and it is in particular open whether it admits an algorithm of complexity O(n) with c < dk2 e. Inspired by an algorithm due to Meiser (1993), we show that there exist linear decision trees and algebraic comp...

The well-known k-SUM conjecture is that integer k-SUM requires time Ω(ndk/2e−o(1)). Recent work has studied multidimensional k-SUM in Fp, where the best known algorithm takes time Õ(ndk/2e). Bhattacharyya et al. [ICS 2011] proved a min(2Ω(d), nΩ(k)) lower bound for k-SUM in Fp under the Exponential Time Hypothesis. We give a more refined lower bound under the standard k-SUM conjecture: for suff...

let $g$ be a connected graph of order $3$ or more and $c:e(g)rightarrowmathbb{z}_k$‎ ‎($kge 2$) a $k$-edge coloring of $g$ where adjacent edges may be colored the same‎. ‎the color sum $s(v)$ of a vertex $v$ of $g$ is the sum in $mathbb{z}_k$ of the colors of the edges incident with $v.$ the $k$-edge coloring $c$ is a modular $k$-edge coloring of $g$ if $s(u)ne s(v)$ in $mathbb{z}_k$ for all pa...

The max-k-sum of a set of real scalars is the maximum sum of a subset of size k, or alternatively the sum of the k largest elements. We study two extensions: First, we show how to obtain smooth approximations to functions that are pointwise max-k-sums of smooth functions. Second, we discuss how the max-k-sum can be defined on vectors in a finite-dimensional real vector space ordered by a closed...