L(2,1,1)-Labeling of Circular-Arc Graphs

Graph labeling problem has been broadly studied in recent past for its wide applications, in mobile communication system for frequency assignment, radar, circuit design, X-ray crystallography, coding theory, etc. An L211-labeling (L211L) of a graph G = (V, E) is a function γ : V → Z∗ such that |γ(u) − γ(v)| ≥ 2, if d(u, v) = 1 and |γ(u) − γ(v)| ≥ 1, if d(u, v) = 1 or 2, where Z∗ be the set of non-negative integers and d(u, v) represents the distance between the nodes u and v. The L211L numbers of a graph G, are denoted by λ2,1,1(G) which is the difference between largest and smallest labels used in L211L. In this article, for circular-arc graph (CAG) G we have proved that λ2,1,1(G) ≤ 6∆ − 4, where ∆ represents the degree of the graph. Beside this we have designed a polynomial time algorithm to label a CAG satisfying the conditions of L211L. The time complexity of the algorithm is O(n∆2), where n is the number of nodes of the graph G.

Statistical tuning of cost 231 Hata model in deployed 1800mhz GSM networks for a rural environment

Radio propagation planning requires the use of propagation models in planning cell size as well as frequency assignment. This paper presents a comparative study of path loss predicted using COST 231 Hata model and ECC-33 model on received signal strength data collected from three deployed GSM networks at 1800MHz in Nigerian Institute for Oil Palm Research environment (NIFOR), Edo State, Nigeria. Based on the Mean Prediction Error (MPE) and Root Mean Square Error (RMSE) values obtained from the comparison, the COST 231 Hata model was tuned using the least square approach. The result obtained after tuning shows that for Network A; MPE andRMSE values reduces to 1.17 dB and 5.5dB. For Network B, MPE and RMSE values reduces to 2.26 dB and 7.16dB. While, for Network C; MPE and RMSE values reduces to 6.21 dB and 10.78dB. The results obtained show that the tuned COST 231 Hata model can be used for radio planning in the study environment as well as other environment with similar terrain profile. Keywords: Propagation model, Path loss, COST 231 Hata model, ECC-33 model, Least square tuning approach, MPE and RMSE

Ant Decision Systems for Combinatorial Optimization with Binary Constraints

In this paper is considered a problem (P) which consists in minimizing an objective function f while satisfying a set of binary constraints. Function f consists in minimizing the number of constraints violations. Problem (P) is NP-hard and has many applications in various fields (e.g., graph coloring, frequency assignment, satellite range scheduling). On the contrary to exact methods, metaheuristics are appropriate algorithms to tackle medium and large sized instances of (P). A specific type of ant metaheuristics is designed to tackle (P), where in contrast with state-of-the-art ant algorithms, an ant is a decision helper and not a constructive procedure.