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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
Approximation Algorithms for Disjoint Paths Problems
, 1996
"... The construction of disjoint paths in a network is a basic issue in combinatorial optimization: given a network, and specified pairs of nodes in it, we are interested in finding disjoint paths between as many of these pairs as possible. This leads to a variety of classical NPcomplete problems for w ..."
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Cited by 157 (0 self)
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The construction of disjoint paths in a network is a basic issue in combinatorial optimization: given a network, and specified pairs of nodes in it, we are interested in finding disjoint paths between as many of these pairs as possible. This leads to a variety of classical NPcomplete problems for which very little is known from the point of view of approximation algorithms. It has recently been brought into focus in work on problems such as VLSI layout and routing in highspeed networks; in these settings, the current lack of understanding of the disjoint paths problem is often an obstacle to the design of practical heuristics.
Adversarial queueing theory
 In Proc. 28th ACM STOC
, 1996
"... We introduce a new approach to the study of dynamic (or continuous) packet routing, where packets are being continuously injected into a network. Our objective is to study what happens to packet routing under continuous injection ..."
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Cited by 111 (6 self)
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We introduce a new approach to the study of dynamic (or continuous) packet routing, where packets are being continuously injected into a network. Our objective is to study what happens to packet routing under continuous injection
Fixedparameter tractability and completeness II: On completeness for W[1]
, 1995
"... For many fixedparameter problems that are trivially solvable in polynomialtime, such as kDOMINATING SET, essentially no better algorithm is presently known than the one which tries all possible solutions. Other problems, such as FEEDBACK VERTEX SET, exhibit fixedparameter tractability: for each ..."
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Cited by 107 (11 self)
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For many fixedparameter problems that are trivially solvable in polynomialtime, such as kDOMINATING SET, essentially no better algorithm is presently known than the one which tries all possible solutions. Other problems, such as FEEDBACK VERTEX SET, exhibit fixedparameter tractability: for each fixed k the problem is solvable in time bounded by a polynomial of degree c, where c is a constant independent of k. In a previous paper, the W Hierarchy of parameterixed problems was defined, and complete problems were identified for the classes W[t] for t >= 2. Our main result shows that INDEPENDENT SET is complete for W[1].
Deciding FirstOrder Properties of Locally TreeDecomposable Graphs
 In Proc. 26th ICALP
, 1999
"... . We introduce the concept of a class of graphs being locally treedecomposable. There are numerous examples of locally treedecomposable classes, among them the class of planar graphs and all classes of bounded valence or of bounded treewidth. We show that for each locally treedecomposable cl ..."
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. We introduce the concept of a class of graphs being locally treedecomposable. There are numerous examples of locally treedecomposable classes, among them the class of planar graphs and all classes of bounded valence or of bounded treewidth. We show that for each locally treedecomposable class C of graphs and for each property ' of graphs that is denable in rstorder logic, there is a linear time algorithm deciding whether a given graph G 2 C has property '. 1 Introduction It is an important task in the theory of algorithms to nd feasible instances of otherwise intractable algorithmic problems. A notion that has turned out to be extremely useful in this context is that of treewidth of a graph. 3Colorability, Hamiltonicity, and many other NPcomplete properties of graphs can be decided in linear time when restricted to graphs whose treewidth is bounded by a xed constant (see [Bod97] for a survey). Courcelle [Cou90] proved a metatheorem, which easily implies numer...
Finding Odd Cycle Transversals
, 2003
"... We present an O(mn) algorithm to determine whether a graph G with m edges and n vertices has an odd cycle cover of order at most k, for any fixed k. We also obtain an algorithm that determines, in the same time, whether a graph has a half integral packing of odd cycles of weight k. ..."
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Cited by 88 (2 self)
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We present an O(mn) algorithm to determine whether a graph G with m edges and n vertices has an odd cycle cover of order at most k, for any fixed k. We also obtain an algorithm that determines, in the same time, whether a graph has a half integral packing of odd cycles of weight k.
Connectivity and Inference Problems for Temporal Networks
 J. Comput. Syst. Sci
, 2000
"... Many network problems are based on fundamental relationships involving time. Consider, for example, the problems of modeling the flow of information through a distributed network, studying the spread of a disease through a population, or analyzing the reachability properties of an airline timetable. ..."
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Cited by 80 (3 self)
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Many network problems are based on fundamental relationships involving time. Consider, for example, the problems of modeling the flow of information through a distributed network, studying the spread of a disease through a population, or analyzing the reachability properties of an airline timetable. In such settings, a natural model is that of a graph in which each edge is annotated with a time label specifying the time at which its endpoints “communicated. ” We will call such a graph a temporal network. To model the notion that information in such a network “flows ” only on paths whose labels respect the ordering of time, we call a path timerespecting if the time labels on its edges are nondecreasing. The central motivation for our work is the following question: how do the basic combinatorial and algorithmic properties of graphs change when we impose this additional temporal condition? The notion of a path is intrinsic to many of the most fundamental algorithmic problems on graphs; spanning trees, connectivity, flows, and cuts are some examples. When we focus on timerespecting paths in place of arbitrary paths, many of these problems acquire a character that is different from the
Efficient and Constructive Algorithms for the Pathwidth and Treewidth of Graphs
, 1993
"... In this paper we give, for all constants k, l, explicit algorithms, that given a graph G = (V; E) with a treedecomposition of G with treewidth at most l, decide whether the treewidth (or pathwidth) of G is at most k, and if so, find a treedecomposition or (pathdecomposition) of G of width at most ..."
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Cited by 77 (13 self)
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In this paper we give, for all constants k, l, explicit algorithms, that given a graph G = (V; E) with a treedecomposition of G with treewidth at most l, decide whether the treewidth (or pathwidth) of G is at most k, and if so, find a treedecomposition or (pathdecomposition) of G of width at most k, and that use O(V) time. In contrast with previous solutions, our algorithms do not rely on nonconstructive reasoning, and are single exponential in k and l. This result can be combined with a result of Reed [37], yielding explicit O(n log n) algorithms for the problem, given a graph G, to determine whether the treewidth (or pathwidth) of G is at most k, and if so, to find a tree (or path)decomposition of width at most k (k constant). Also, Bodlaender [13] has used the result of this paper to obtain linear time algorithms for these problems. We also show that for all constants k, there exists a polynomial time algorithm, that, when given a graph G = (V; E) with treewidth k, computes the pathwidth of G and a minimum path decomposition of G.