Miri Priesler - Academia.edu (original) (raw)

Papers by Miri Priesler

Research paper thumbnail of Multigraph decomposition into multigraphs with two underlying edges

Discrete Mathematics & Theoretical Computer Science

Due to some intractability considerations, reasonable formulation of necessary and sufficient con... more Due to some intractability considerations, reasonable formulation of necessary and sufficient conditions for decomposability of a general multigraph G into a fixed connected multigraph H, is probably not feasible if the underlying simple graph of H has three or more edges. We study the case where H consists of two underlying edges. We present necessary and sufficient conditions for H-decomposability of G, which hold when certain size parameters of G lies within some bounds which depends on the multiplicities of the two edges of H. We also show this result to be "tight" in the sense that even a slight deviation of these size parameters from the given bounds results intractability of the corresponding decision problem.

Research paper thumbnail of Time and Frequency Resource Allocation using Graph Theory in OFDMA Wireless Mesh Networks

A wireless network with a mesh topology works reliably and offers redundancy. In modern broadband... more A wireless network with a mesh topology works reliably and offers redundancy. In modern broadband wireless mesh networks that use MIMO and OFDMA techniques, the problems of time, frequency, and space resource allocations are different from a cellular system and more complicated due to system architecture and distributed control and management. This paper focuses on the resource allocation problem of the OFDMA system and we define the term of separability order. For simple topologies like the square grid configuration, the allocations are simple and an optimal solution can be shown, but for an arbitrary architecture we need advanced tools and we use Graph Theory tools to present two different algorithmic solutions, to allow frequency reuse.

Research paper thumbnail of Resource Allocation in Wireless Mesh Networks

Journal of Ambient Wireless Communications and Smart Environments (AMBIENTCOM), 2016

A wireless network with a mesh topology works reliably and offers redundancy. In modern broadband... more A wireless network with a mesh topology works reliably and offers redundancy. In modern broadband wireless mesh networks using MIMO and OFDMA techniques, the problems of time, frequency, and space resource allocations, synchronization, and routing, are not only different from a cellular system, they are more complicated due to system architecture and distributed control and management. This paper focuses on OFDMA wireless mesh network systems and the problem of time/frequency resource allocation, particularly with regard to subcarriers. The term of separability order is defined. For simple topologies such as the square grid configuration, the allocations are relatively simple, and optimal solutions can be demonstrated, but in an arbitrary architecture advanced graph theory tools are required in order to present an algorithmic solution to resource allocation and allow frequency reuse.

Research paper thumbnail of Time and Frequency Resource Allocation in OFDMA Wireless Mesh Networks

Research paper thumbnail of Distributed network synchronization

2015 IEEE International Conference on Microwaves, Communications, Antennas and Electronic Systems (COMCAS), 2015

This paper presents a non centralized, non hierarchical and distributed synchronization process f... more This paper presents a non centralized, non hierarchical and distributed synchronization process for wireless mesh networks. Each node has a time base that relative to an universal clock has an offset and a clock frequency difference and the purpose of the synchronization is to correct the offset and the frequency so all the nodes will have almost the same time base. The synchronization process is based on periodically transmission of messages with timing information by the all the nodes. The timing messages can be retransmitted to other nodes. Each node is correcting his time base according to the received messages. The synchronization process has an acquisition phase when the clocks of the nodes have large variations and when the variations are reduced below a certain threshold the synchronization process switches to the tracking phase. In the tracking phase the variations among nodes are farther reduced and the changes in clock parameters are followed. Synchronization algorithms and simulation results are presented.

Research paper thumbnail of Multigraph decomposition into stars and into multistars

Discrete Mathematics, 2005

We study the decomposition of multigraphs with a constant edge multiplicity into copies of a fixe... more We study the decomposition of multigraphs with a constant edge multiplicity into copies of a fixed star H = K 1,t : We present necessary and sufficient conditions for such a decomposition to exist where t = 2 and prove NP-completeness of the corresponding decision problem for any t 3. We also prove NP-completeness when the edge multiplicity function is not restricted either on the input G or on the fixed multistar H.

Research paper thumbnail of On some multigraph decomposition problems and their computational complexity

Discrete Mathematics, 2004

Let H be a ÿxed simple graph. The H-decomposition computational problem is deÿned as follows: Giv... more Let H be a ÿxed simple graph. The H-decomposition computational problem is deÿned as follows: Given an input graph G, can its edge set be partitioned into isomorphic copies of H ? The complexity status of H-decomposition problems, where no parallel edges or loops are allowed in G or in H , has been thoroughly studied during the last 20 years and is now completely settled. The subject of this article is the complexity of multigraph decomposition, that is the case where multiple edges are allowed. Apparently, the results obtained here are not always what one would expect by observing the analogous results on simple graphs. For example, deciding whether an input graph G, with ÿxed multiplicity on all edges, can be decomposed into connected subgraphs, each consisting of two distinct edges with multiplicities 1 on one edge and 2 on the other, is NP-complete if = 2 or 5 and it is solvable in polynomial time for any other values of .

Research paper thumbnail of Partitioning a graph into two pieces, each isomorphic to the other or to its complement

Discrete Mathematics, 2005

A simple graph G has the generalized-neighbour-closed-co-neighbour property, or is a gncc graph, ... more A simple graph G has the generalized-neighbour-closed-co-neighbour property, or is a gncc graph, if for all vertices x of G, the subgraph, induced by the set of neighbours of x, is isomorphic to the subgraph, induced by the set of non-neighbours of x, or is isomorphic to its complement. If every vertex x satisfies the first condition (that is, the subgraphs, induced by its set of neighbours, and by its set of non-neighbours, are isomorphic), then the graph has the neighbour-closed-co-neighbour property, or is an ncc graph. In [A. Bonato, R. Nowakowski, Partitioning a graph into two isomorphic pieces, J. Graph Theory, 44 (2003) 1-14], the ncc graphs were characterized and a polynomial time algorithm was given for their recognition. In this paper we show that all gncc graphs are also ncc, that is, we prove that the two families of graphs, defined above, are identical. Finally, we present some of the properties of an interesting family of graphs, that is derived from the proof of the claim above, and we give a polynomial time algorithm to recognize such graphs.

Research paper thumbnail of Multigraph decomposition into multigraphs with two underlying edges

Discrete Mathematics & Theoretical Computer Science

Due to some intractability considerations, reasonable formulation of necessary and sufficient con... more Due to some intractability considerations, reasonable formulation of necessary and sufficient conditions for decomposability of a general multigraph G into a fixed connected multigraph H, is probably not feasible if the underlying simple graph of H has three or more edges. We study the case where H consists of two underlying edges. We present necessary and sufficient conditions for H-decomposability of G, which hold when certain size parameters of G lies within some bounds which depends on the multiplicities of the two edges of H. We also show this result to be "tight" in the sense that even a slight deviation of these size parameters from the given bounds results intractability of the corresponding decision problem.

Research paper thumbnail of Time and Frequency Resource Allocation using Graph Theory in OFDMA Wireless Mesh Networks

A wireless network with a mesh topology works reliably and offers redundancy. In modern broadband... more A wireless network with a mesh topology works reliably and offers redundancy. In modern broadband wireless mesh networks that use MIMO and OFDMA techniques, the problems of time, frequency, and space resource allocations are different from a cellular system and more complicated due to system architecture and distributed control and management. This paper focuses on the resource allocation problem of the OFDMA system and we define the term of separability order. For simple topologies like the square grid configuration, the allocations are simple and an optimal solution can be shown, but for an arbitrary architecture we need advanced tools and we use Graph Theory tools to present two different algorithmic solutions, to allow frequency reuse.

Research paper thumbnail of Resource Allocation in Wireless Mesh Networks

Journal of Ambient Wireless Communications and Smart Environments (AMBIENTCOM), 2016

A wireless network with a mesh topology works reliably and offers redundancy. In modern broadband... more A wireless network with a mesh topology works reliably and offers redundancy. In modern broadband wireless mesh networks using MIMO and OFDMA techniques, the problems of time, frequency, and space resource allocations, synchronization, and routing, are not only different from a cellular system, they are more complicated due to system architecture and distributed control and management. This paper focuses on OFDMA wireless mesh network systems and the problem of time/frequency resource allocation, particularly with regard to subcarriers. The term of separability order is defined. For simple topologies such as the square grid configuration, the allocations are relatively simple, and optimal solutions can be demonstrated, but in an arbitrary architecture advanced graph theory tools are required in order to present an algorithmic solution to resource allocation and allow frequency reuse.

Research paper thumbnail of Time and Frequency Resource Allocation in OFDMA Wireless Mesh Networks

Research paper thumbnail of Distributed network synchronization

2015 IEEE International Conference on Microwaves, Communications, Antennas and Electronic Systems (COMCAS), 2015

This paper presents a non centralized, non hierarchical and distributed synchronization process f... more This paper presents a non centralized, non hierarchical and distributed synchronization process for wireless mesh networks. Each node has a time base that relative to an universal clock has an offset and a clock frequency difference and the purpose of the synchronization is to correct the offset and the frequency so all the nodes will have almost the same time base. The synchronization process is based on periodically transmission of messages with timing information by the all the nodes. The timing messages can be retransmitted to other nodes. Each node is correcting his time base according to the received messages. The synchronization process has an acquisition phase when the clocks of the nodes have large variations and when the variations are reduced below a certain threshold the synchronization process switches to the tracking phase. In the tracking phase the variations among nodes are farther reduced and the changes in clock parameters are followed. Synchronization algorithms and simulation results are presented.

Research paper thumbnail of Multigraph decomposition into stars and into multistars

Discrete Mathematics, 2005

We study the decomposition of multigraphs with a constant edge multiplicity into copies of a fixe... more We study the decomposition of multigraphs with a constant edge multiplicity into copies of a fixed star H = K 1,t : We present necessary and sufficient conditions for such a decomposition to exist where t = 2 and prove NP-completeness of the corresponding decision problem for any t 3. We also prove NP-completeness when the edge multiplicity function is not restricted either on the input G or on the fixed multistar H.

Research paper thumbnail of On some multigraph decomposition problems and their computational complexity

Discrete Mathematics, 2004

Let H be a ÿxed simple graph. The H-decomposition computational problem is deÿned as follows: Giv... more Let H be a ÿxed simple graph. The H-decomposition computational problem is deÿned as follows: Given an input graph G, can its edge set be partitioned into isomorphic copies of H ? The complexity status of H-decomposition problems, where no parallel edges or loops are allowed in G or in H , has been thoroughly studied during the last 20 years and is now completely settled. The subject of this article is the complexity of multigraph decomposition, that is the case where multiple edges are allowed. Apparently, the results obtained here are not always what one would expect by observing the analogous results on simple graphs. For example, deciding whether an input graph G, with ÿxed multiplicity on all edges, can be decomposed into connected subgraphs, each consisting of two distinct edges with multiplicities 1 on one edge and 2 on the other, is NP-complete if = 2 or 5 and it is solvable in polynomial time for any other values of .

Research paper thumbnail of Partitioning a graph into two pieces, each isomorphic to the other or to its complement

Discrete Mathematics, 2005

A simple graph G has the generalized-neighbour-closed-co-neighbour property, or is a gncc graph, ... more A simple graph G has the generalized-neighbour-closed-co-neighbour property, or is a gncc graph, if for all vertices x of G, the subgraph, induced by the set of neighbours of x, is isomorphic to the subgraph, induced by the set of non-neighbours of x, or is isomorphic to its complement. If every vertex x satisfies the first condition (that is, the subgraphs, induced by its set of neighbours, and by its set of non-neighbours, are isomorphic), then the graph has the neighbour-closed-co-neighbour property, or is an ncc graph. In [A. Bonato, R. Nowakowski, Partitioning a graph into two isomorphic pieces, J. Graph Theory, 44 (2003) 1-14], the ncc graphs were characterized and a polynomial time algorithm was given for their recognition. In this paper we show that all gncc graphs are also ncc, that is, we prove that the two families of graphs, defined above, are identical. Finally, we present some of the properties of an interesting family of graphs, that is derived from the proof of the claim above, and we give a polynomial time algorithm to recognize such graphs.