Mehmet Hakan Karaata

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This paper describes an algorithm for coloring the nodes of a planar graph with no more than six colors using a self-stabilizing approach. The first part illustrates the coloring algorithm on a directed acyclic version of the given planar graph. The second part describes a selfstabilizing algorithm for generating the directed acyclic version of the planar(More)
Let T = (V, 1?) be a tree. The eccentricity of a vertex i E V is the largest distance from i to any vertex in V. A vertex with minimum eccentricity is called a center of T. The wezght of a vertex i E V is the sum of the distances from i to all other vertices in I,’. A vertex with minimum weight. is called a median of T. We present simple, self-stabilizing(More)
Dynamic programming is a bottom-up approach that is typically used for designing algorithms for optimization problems. Many graph-theoretic optimization problems that are NP-hard in general, can be eeciently solved, using dynamic programming, when restricted to trees. Examples of such problems include maximum weighted independent set and minimum weighted(More)
A self-stabilizing algorithm is presented in this paper that finds the bridges of a connected undirected graph on a distributed or network model of computation after $O(\vert E\vert n^2)$ moves. The algorithm is resilient to transient faults and does not require initialization. In addition, a correctness proof of the algorithm is provided. The paper(More)
In this paper, a self-stabilizing algorithm is presented for finding biconnected components of a connected undirected graph on a distributed or network model of computation. The algorithm is resilient to transient faults, therefore, it does not require initialization. The proposed algorithm is based on stabilizing BFS construction and bridge-finding(More)
The node-disjoint paths problem deals with finding node-disjoint paths from a source node s to target node t, where t ¿ s. Two paths from s to t are said to be node-disjoint iff they do not have any common vertices except for their endpoints. Distributed solutions to the node-disjoint paths problem have numerous applications such as secure message(More)
In real-time systems, correct information is needed fast, so developing fast and accurate algorithms is a must. Algorithms must be resilient to transient faults and topology changes. The capability to adapt to heterogeneous and changing requirements is the core of assurance in distributed systems. A snap-stabilizing algorithm, starting from an arbitrary(More)
Self-stabilization is a novel technique to deal with faults in distributed systems. This paper presents a distributed self-stabilizing algorithm for implementing strong fairness in an arbitrary network. A desirable feature of this algorithm is that it can be used to enforce the strong fairness property on any distributed algorithm including self-stabilizing(More)