1. Two Connected Dominating Set Algorithms for Wireless Sensor Networks Overview Najla Al-Nabhan* ♦ Bowu Zhang** ♦ Mznah Al-Rodhaan* ♦ Abdullah Al-Dhelaan* The Proposed Algorithms  Connected Dominating Set (CDS)  CDS is known to be an efficient strategy to control network topology, reduce overhead, and extend network lifetime.  CDS finds a minimum size subset of nodes that can collaboratively form a virtual backbone.  Definition  For a given connected graph (network) G = (V, E), a dominating set (DS) is a subset V' of V, where for each vertex (node) u of V, u is either in V' or at least one neighbor vertex of u is in V'. A DS is called a CDS if the sub-graph induced by the vertices in the DS is connected.  In this work, we present the design of two novel algorithms for CDS construction in WSNs.  Our algorithms are intended to minimize CDS size. The first algorithm has a performance factor of 5 from the optimal solution, which outperforms the best-published results (S-MIS algorithm) that has a performance factor = 5.8+ ln 4. The second algorithm is an improved version of the first algorithm. Approach-I 2.The newly colored black node (u ) dominates its 1-hop yellow, orange, and white nodes by coloring them gray. Furthermore, u marks its 2-hop white/orange nodes into yellow; and marks its 3-hops white nodes into orange. Approach-I Approach-II  Approach-II also has 4 phases. Phase-1, 3, and 4 are similar to their corresponding phases in Approach-I.  In Phase-2, we define the coverage factor of a yellow/gray node x as the number of its yellow neighbors. A gray/yellow node x that has the highest coverage factor is marked red. Then, x dominates its 1-hop yellow neighbors by coloring them gray.  In Phase-3: If a gray node u was marked red in Phase-2 of this approach, u is already connected to an S 1 node and we do not need to introduce any connectors for u. Simulation Results  N [ 36,400 ], the transmission range of each node R [200, 800], and the considered deployment schemes are: the uniform random and the partial random deployment models.  Results show that the sizes of CDSs generated by Approach-I and Approach-II are smaller than S-MIS as the network size increases.  Approach-II always outperforms both Approach-I and S-MIS in uniform random and grid-based deployments, and for small and large-scale networks.  To implement distributed versions of the proposed algorithms.  To introduce more performance improvements. Future Work  Approach-I consists of 4 main phases to construct a CDS:  Phase-1: S1 Construction  given an arbitrary rooted spanning tree T, we define the tree level of a node u as the number of hops in T between u itself and i, where i is the root of T. All nodes are initially undominated and colored white.  The root node (i) initiates S 1 construction by coloring itself black. Then: all white nodes that are 1-hop from i are colored gray; all white nodes that are 2-hop from i are colored yellow; all white nodes that are 3-hop from i are colored orange.  Next, the algorithm repeats the following steps until no orange/white nodes left in the graph. 1.Selects an orange node u to color it black. The selected orange node satisfies the following two conditions: i) its level is the lowest (closes to the root) among all orange nodes, and ii) it has the maximum number of 3-hop black neighbors. The selected node u is colored black.  We model a WSN using a unit disk graph (UDG).  We simplify the CDS construction by first finding a special independent set S 1 satisfying the following condition: the hop-distance between any two complementary subsets S’ and S” of S 1 is exactly three.  Second, we find a small set of nodes S 2 to dominate the multiple disconnected components resulted from constructing S 1 in the first step.  Then, nodes in S 2 are connected with nodes in S 1 in order to form the final CDS by adding more connecting nodes.  The above described technique is performed in two different ways in Approach-I and Approach-II.  For illustration purpose, we employ a coloring scheme to differentiate node states during the construction process.  Dominators (S 1 ): black, dominatee: gray, (S 1 ): red, connectors: blue. Other colors are temporary colors. *{nalnabhan,rodhaan,dhelaan}@ksu.edu.sa, **{bowuzh}@gwmail.gwu.edu  Phase-2: Covering Disconnected Regions (CDC)  We optimally compute a minimum dominating set for each connected yellow component. All the dominators computed from this phase are colored red and they form the set S 2.  Phase-3: Connecting S 2 Nodes to S 1 Nodes.  Phase-4: Connecting S 1 Nodes all Together. An exemplary graph G of 40 nodes after S 1 construction Performance Analysis  Given any Minimum CDS (MCDS) of a unit-disk graph G, we show that: Approach-I produces a CDS with a size bounded by 5opt, where opt is the size of the MCDS. The proof of this theorem is provided in the paper.  For the simulation, we focused on CDS size as the main and most important performance measure.  We generated a total of N nodes in a fixed 1000*1000 2D square. Random network of 70 nodes Node density [28, 346] N [36, 225], R=400