: Significant progress has been made with solution of location problems and in preprocessing and decomposition for discrete optimization. There has also been research on the application of techniques from combinational optimization to nonlinear problems.

http://www.dtic.mil/dtic/tr/fulltext/u2/a273552.pdf

Discrete Applied Mathematics

Given any fixed non-negative integer values h and k, the L(h, k)-labelling problem consists in an assignment of non-negative integers to the nodes of a graph such that adjacent nodes receive values which differ by at least h, and nodes connected by a 2-length path receive values which differ by at least k. The span of an L(h, k)-labelling is the difference between the largest and the smallest assigned frequency. The goal of the problem is to find out an L(h, k)-labelling with a minimum span. The L(h, k)-labelling problem has intensively been studied following many approaches and restricted to many special cases, concerning both the values of h and k and the considered classes of graphs. This paper reviews the results from previously published literature, looking at the problem with a graph algorithmic approach. It is an update of a previous survey written by the same author.

/pdf/the-l-h-k-labelling-problem-2n6x162uc0.pdf

The L(h, k)-Labelling Problem

People are always concerned about privacy. Techniques tracing specific user activities may damage privacy seriously. To protect user privacy, a dynamic-identity-based remote user authentication scheme will be proposed in this manuscript. This scheme employs smart cards to achieve mutual authentication, and no verifier table is needed. Via this scheme, transmitted identities are always fresh such that untraceability is ensured, and a user can change his or her password after being authenticated successfully. Copyright © 2013 John Wiley & Sons, Ltd.

Untraceable dynamic-identity-based remote user authentication scheme with verifiable password update

A discussion on the relationship between probabilistic visual cryptography and random grid

In this paper, to address the issue of demand response in the smart grid with island MicroGrids (MGs), we introduce an effective and secure auction market that allows electric vehicles (EVs) having surplus energy to act as sellers, and the EVs having insufficient energy in the island MGs to act as buyers. There are two primary challenges in designing an effective auction market in the smart grid. First, the auction market scheme shall be online, allowing buyers and sellers to enter the market at any time, and satisfy several critical economic properties (individual rationality, incentive compatibility, and so on.). Second, the sensitive information of participants shall be protected in the auction process. To address these challenges, we present a novel privacy-preserving online double auction scheme based on differential privacy. In our auction market, the MicroGrid Center Controller (MGCC) acts as the auctioneer, aiming at solving the social welfare maximization problem to match buyers and sellers. The principle of differential privacy is leveraged to protect the privacy of EVs’ sensitive bidding information. Via theoretical analysis, we demonstrate that our designed auction scheme satisfies both economic and privacy-preserving properties, including individual rationality, incentive compatibility, weak budget balance, and $\varepsilon $ -differential privacy. We conduct an extensive performance evaluation to measure the effectiveness of our proposed scheme. Our experimental results show that the proposed auction scheme can not only ensure the privacy of participants but also effectively facilitates demand response in the smart grid, with respect to social welfare, satisfaction ratio, social efficiency, and computational overhead.

Towards Differential Privacy-Based Online Double Auction for Smart Grid

In this paper, we consider two embedding problems in Cartesian product networks: one is the pancycle problem, which involves embedding cycles of various lengths in the given product network; and the other is the panconnectivity problem, which involves embedding paths of various lengths between any pair of distinct nodes in the given product network. We then apply our technical lemmas and theorems to derive new topological properties of two multiprocessor systems, namely, generalized hypercubes and nearest neighbor mesh hypercubes.

Embedding Cycles and Paths in Product Networks and Their Applications to Multiprocessor Systems

Practical electronic auction scheme with strong anonymity and bidding privacy

Quality-adaptive visual secret sharing by random grids

Let G be a graph with diameter d. An antipodal labeling of G is a function f that assigns to each vertex a non-negative integer (label) such that for any two vertices u and v, it is satisfied that |f(u) − f(v)| ≥ d − d(u, v), where d(u, v) is the distance between u and v. The span of an antipodal labeling f is max{f(u) − f(v) : u, v ∈ V (G)}. The antipodal number for G, denoted by an(G), is the minimum span of an antipodal labeling for G. Let Cn denote the cycle on n vertices. Chartrand, Erwin and Zhang [4] determined the value of an(Cn) for n ≡ 2 (mod 4). In this article we determine the value of an(Cn) for n ≡ 1 (mod 4), confirming a conjecture of Chartrand el al. Moreover, we settle the case n ≡ 3 (mod 4); and improve the known lower bound and give an upper bound for the case n ≡ 0 (mod 4).

Antipodal Labelings for Cycles.

Given an edge-weighted undirected graph G and two prescribed vertices u and v, a next-to-shortest (u,v)-path is a shortest (u,v)-path amongst all (u,v)-paths having length strictly greater than the length of a shortest (u,v)-path. In this paper, we deal with the problem of computing a next-to-shortest (u,v)-path. We propose an ${\mathcal{O}}(n^{2})$ time algorithm for solving this problem, which significantly improves the bound of a previous one in ${\mathcal{O}}(n^{3})$ time where n is the number of vertices in G.

Justie Su-Tzu Juan

Papers

Embedding Cycles and Paths in Product Networks and Their Applications to Multiprocessor Systems

Practical electronic auction scheme with strong anonymity and bidding privacy

Quality-adaptive visual secret sharing by random grids

Antipodal Labelings for Cycles.

A Quadratic Algorithm for Finding Next-to-Shortest Paths in Graphs