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28
The NPcompleteness column: an ongoing guide
 JOURNAL OF ALGORITHMS
, 1987
"... This is the nineteenth edition of a (usually) quarterly column that covers new developments in the theory of NPcompleteness. The presentation is modeled on that used by M. R. Garey and myself in our book "Computers and Intractability: A Guide to the Theory of NPCompleteness," W. H. Freem ..."
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This is the nineteenth edition of a (usually) quarterly column that covers new developments in the theory of NPcompleteness. The presentation is modeled on that used by M. R. Garey and myself in our book "Computers and Intractability: A Guide to the Theory of NPCompleteness," W. H. Freeman & Co., New York, 1979 (hereinafter referred to as "[G&J]"; previous columns will be referred to by their dates). A background equivalent to that provided by [G&J] is assumed, and, when appropriate, crossreferences will be given to that book and the list of problems (NPcomplete and harder) presented there. Readers who have results they would like mentioned (NPhardness, PSPACEhardness, polynomialtimesolvability, etc.) or open problems they would like publicized, should
A dynamic survey of graph labellings
 Electron. J. Combin., Dynamic Surveys(6):95pp
, 2001
"... A graph labeling is an assignment of integers to the vertices or edges, or both, subject to certain conditions. Graph labelings were first introduced in the late 1960s. In the intervening years dozens of graph labelings techniques have been studied in over 1000 papers. Finding out what has been done ..."
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A graph labeling is an assignment of integers to the vertices or edges, or both, subject to certain conditions. Graph labelings were first introduced in the late 1960s. In the intervening years dozens of graph labelings techniques have been studied in over 1000 papers. Finding out what has been done for any particular kind of labeling and keeping up with new discoveries is difficult because of the sheer number of papers and because many of the papers have appeared in journals that are not widely available. In this survey I have collected everything I could find on graph labeling. For the convenience of the reader the survey includes a detailed table of contents and index.
Network file storage with graceful performance degradation
 ACM Transactions on Storage
, 2005
"... A file storage scheme is proposed for networks containing heterogeneous clients. In the scheme, the performance measured by fileretrieval delays degrades gracefully under increasingly serious faulty circumstances. The scheme combines coding with storage for better performance. The problem is NPhar ..."
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A file storage scheme is proposed for networks containing heterogeneous clients. In the scheme, the performance measured by fileretrieval delays degrades gracefully under increasingly serious faulty circumstances. The scheme combines coding with storage for better performance. The problem is NPhard for general networks; and this paper focuses on tree networks with asymmetric edges between adjacent nodes. A polynomialtime memoryallocation algorithm is presented, which determines how much data to store on each node, with the objective of minimizing the total amount of data stored in the network. Then a polynomialtime datainterleaving algorithm is used to determine which data to store on each node for satisfying the qualityofservice requirements in the scheme. By combining the memoryallocation algorithm with the datainterleaving algorithm, an optimal solution to realize the file storage scheme in tree networks is established.
Algorithmic aspect of ktuple domination in graphs
 Taiwanese J. Math
"... Abstract. In a graph G, a vertex is said to dominate itself and all of its neighbors. For a fixed positive integer k, the ktuple domination problem is to find a minimum sized vertex subset such that every vertex in the graph is dominated by at least k vertices in this set. The present paper studies ..."
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Abstract. In a graph G, a vertex is said to dominate itself and all of its neighbors. For a fixed positive integer k, the ktuple domination problem is to find a minimum sized vertex subset such that every vertex in the graph is dominated by at least k vertices in this set. The present paper studies the ktuple domination problem in graphs from an algorithmic point of view. In particular, we give a lineartime algorithm for the 2tuple domination problem in trees by employing a labeling method. 1.
Clique rDomination and Clique rPacking Problems on Dually Chordal Graphs
, 1997
"... Let be a family of cliques of a graph G =(V,E). Suppose that each clique C of is associated with an integer r(C), where r(C) 0. A vertex vrdominates a clique C of G if d(v, x) r(C) for all x C, where d(v, x) is the standard graph distance. A subset D V is a clique rdominating set ..."
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Let be a family of cliques of a graph G =(V,E). Suppose that each clique C of is associated with an integer r(C), where r(C) 0. A vertex vrdominates a clique C of G if d(v, x) r(C) for all x C, where d(v, x) is the standard graph distance. A subset D V is a clique rdominating set of G if for every clique C is a vertex u D which rdominates C. A clique rpacking set is a subset P that there are no two distinct cliques C # ,C ## Prdominated by a common vertex of G. The clique rdomination problem is to find a clique rdominating set with minimum size and the clique rpacking problem is to find a clique rpacking set with maximum size. The formulated problems include many domination and cliquetransversalrelated problems as special cases. In this paper an efficient algorithm is proposed for solving these problems on dually chordal graphs which are a natural generalization of strongly chordal graphs. The efficient algorithm is mainly based on the tree structure and special vertex elimination orderings of dually chordal graphs. In some important particular cases where the algorithm works in linear time the obtained results generalize and improve known results on strongly chordal graphs.
Broadcast Domination Algorithms for Interval Graphs, SeriesParallel Graphs, and Trees
 Proceedings of the 35th Southeastern International Conference on Combinatorics, Graph Theory, and Computing (CGTC
, 2004
"... Broadcast domination assigns an integer value f(u) 0 to each vertex u of a given graph, such that every vertex u with f(u) = 0 is within distance f(v) from a vertex v with f(v)> 0. We can regard the vertices v with f(v)> 0 as broadcast stations, each having a transmission power that might b ..."
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Broadcast domination assigns an integer value f(u) 0 to each vertex u of a given graph, such that every vertex u with f(u) = 0 is within distance f(v) from a vertex v with f(v)> 0. We can regard the vertices v with f(v)> 0 as broadcast stations, each having a transmission power that might be dierent from the powers of other stations. The optimal broadcast domination problem seeks to minimize the sum of the costs of the broadcasts assigned to the vertices of the graph. We present dynamic programming algorithms that solve the optimal broadcast domination problem for the rst classes of graphs with nontrivial solutions: interval graphs, seriesparallel graphs, and trees. We also show that optimal broadcast domination is equivalent to optimal domination on proper interval graphs. 1 Introduction and
A memory efficient selfstabilizing algorithm for maximal kpacking
 in SSS’06: Proceedings of the 8th international conference on Stabilization, safety, and
, 2006
"... Abstract. The kpacking problem asks for a subset S of the nodes in a graph such that the distance between any pair of nodes in S is greater than k. This problem has applications to placing facilities in a network. In the current paper we present a selfstabilizing algorithm for computing a maximal ..."
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Abstract. The kpacking problem asks for a subset S of the nodes in a graph such that the distance between any pair of nodes in S is greater than k. This problem has applications to placing facilities in a network. In the current paper we present a selfstabilizing algorithm for computing a maximal kpacking in a general graph. Our algorithm uses a constant number of variables per node. This improves the memory requirement compared to the previous most memory efficient algorithm [9] which used k variables per node. In addition the presented algorithm is very short and simple.
Algorithms
"... In the last quarter of the century there has been a growing interest in the design and analysis of algorithms in different branches of mathematics, science and engineering. In particular, within the past 15 years there has appeared a wealth of literature on algorithms in graph theory, a significant ..."
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In the last quarter of the century there has been a growing interest in the design and analysis of algorithms in different branches of mathematics, science and engineering. In particular, within the past 15 years there has appeared a wealth of literature on algorithms in graph theory, a significant part of which is related to domination in graphs. Since there are well over one hundred papers on domination or dominationrelated algorithms, this chapter will necessarily have to focus on a limited collection of these algorithms. The intention of this chapter on domination algorithms for special graph classes is twofold. The major goal is to demonstrate some of the main techniques for designing efficient algorithms for domination problems. For this purpose we consider some particular examples and focus on five graph classes and five well researched variants of the domination problem. Another goal is to present a fairly comprehensive bibliography of algorithms for domination problems. We refer the reader who is unfamiliar with the design and analysis of algorithms to [57].
Optimal broadcast domination in polynomial time
"... Broadcast domination was introduced by Erwin in 2002, and it is a variant of the standard dominating set problem, such that different vertices can be assigned different domination powers. Broadcast domination assigns an integer power f(v) >= 0 to each vertex v of a
given graph, such that every ve ..."
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Broadcast domination was introduced by Erwin in 2002, and it is a variant of the standard dominating set problem, such that different vertices can be assigned different domination powers. Broadcast domination assigns an integer power f(v) >= 0 to each vertex v of a
given graph, such that every vertex of the graph is within distance f(v) from some vertex v having f(v) >= 1. The optimal broadcast domination problem seeks to minimize the sum of the powers assigned to the vertices of the graph. Since the presentation of this problem its computational complexity has been open, and the general belief has
been that it might be NPhard. In this paper, we show that optimal broadcast domination is actually in P, and we give a polynomial time algorithm for solving the problem on arbitrary graphs, using a non standard approach.
Combining visual layout and lexical cohesion features for text segmentation
 In Proceedings of the 31stWorkshop on Graph Theoretic Concepts in Computer Science WG 2005
"... Abstract. Broadcast domination was introduced by Erwin in 2002, and it is a variant of the standard dominating set problem, such that vertices can be assigned various domination powers. Broadcast domination assigns a power f(v) ≥ 0 to each vertex v of a given graph, such that every vertex of the gr ..."
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Abstract. Broadcast domination was introduced by Erwin in 2002, and it is a variant of the standard dominating set problem, such that vertices can be assigned various domination powers. Broadcast domination assigns a power f(v) ≥ 0 to each vertex v of a given graph, such that every vertex of the graph is within distance f(v) from some vertex v having f(v) ≥ 1. The optimal broadcast domination problem seeks to minimize the sum of the powers assigned to the vertices of the graph. Since the presentation of this problem its computational complexity has been open, and the general belief has been that it might be N Phard. In this paper, we show that optimal broadcast domination is actually in P, and we give a polynomial time algorithm for solving the problem on arbitrary graphs, using a non standard approach. 1