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Multilevel hypergraph partitioning: Application in VLSI domain
 IEEE TRANS. VERY LARGE SCALE INTEGRATION (VLSI) SYSTEMS
, 1999
"... In this paper, we present a new hypergraphpartitioning algorithm that is based on the multilevel paradigm. In the multilevel paradigm, a sequence of successively coarser hypergraphs is constructed. A bisection of the smallest hypergraph is computed and it is used to obtain a bisection of the origina ..."
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Cited by 312 (23 self)
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In this paper, we present a new hypergraphpartitioning algorithm that is based on the multilevel paradigm. In the multilevel paradigm, a sequence of successively coarser hypergraphs is constructed. A bisection of the smallest hypergraph is computed and it is used to obtain a bisection of the original hypergraph by successively projecting and refining the bisection to the next level finer hypergraph. We have developed new hypergraph coarsening strategies within the multilevel framework. We evaluate their performance both in terms of the size of the hyperedge cut on the bisection, as well as on the run time for a number of very large scale integration circuits. Our experiments show that our multilevel hypergraphpartitioning algorithm produces highquality partitioning in a relatively small amount of time. The quality of the partitionings produced by our scheme are on the average 6%–23 % better than those produced by other stateoftheart schemes. Furthermore, our partitioning algorithm is significantly faster, often requiring 4–10 times less time than that required by the other schemes. Our multilevel hypergraphpartitioning algorithm scales very well for large hypergraphs. Hypergraphs with over 100 000 vertices can be bisected in a few minutes on today’s workstations. Also, on the large hypergraphs, our scheme outperforms other schemes (in hyperedge cut) quite consistently with larger margins (9%–30%).
A sufficient condition for backtrackfree search
, 1982
"... A constraint satisfaction problem revolves finding values for a set of variables subject of a set of constraints (relations) on those variables Backtrack search is often used to solve such problems. A relationship involving the structure of the constraints i described which characterizes tosome deg ..."
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Cited by 297 (14 self)
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A constraint satisfaction problem revolves finding values for a set of variables subject of a set of constraints (relations) on those variables Backtrack search is often used to solve such problems. A relationship involving the structure of the constraints i described which characterizes tosome degree the extreme case of mimmum backtracking (none) The relationship involves a concept called "width," which may provide some guidance in the representation f constraint satisfaction problems and the order m which they are searched The width concept is studied and applied, in particular, to constraints which form tree structures.
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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Cited by 242 (0 self)
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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
Approximate graph coloring by semidefinite programming
 Proc. 35 th IEEE FOCS, IEEE
, 1994
"... a coloring is called the chromatic number of�, and is usually denoted by��.Determining the chromatic number of a graph is known to be NPhard (cf. [19]). Besides its theoretical significance as a canonical NPhard problem, graph coloring arises naturally in a variety of applications such as register ..."
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Cited by 212 (6 self)
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a coloring is called the chromatic number of�, and is usually denoted by��.Determining the chromatic number of a graph is known to be NPhard (cf. [19]). Besides its theoretical significance as a canonical NPhard problem, graph coloring arises naturally in a variety of applications such as register allocation [11, 12, 13] is the maximum degree of any vertex. Beand timetable/examination scheduling [8, 40]. In many We consider the problem of coloring�colorable graphs with the fewest possible colors. We give a randomized polynomial time algorithm which colors a 3colorable graph on vertices with� � ���� colors where sides giving the best known approximation ratio in terms of, this marks the first nontrivial approximation result as a function of the maximum degree. This result can be generalized to�colorable graphs to obtain a coloring using�� � ��� � � � �colors. Our results are inspired by the recent work of Goemans and Williamson who used an algorithm for semidefinite optimization problems, which generalize linear programs, to obtain improved approximations for the MAX CUT and MAX 2SAT problems. An intriguing outcome of our work is a duality relationship established between the value of the optimum solution to our semidefinite program and the Lovász�function. We show lower bounds on the gap between the optimum solution of our semidefinite program and the actual chromatic number; by duality this also demonstrates interesting new facts about the�function. 1
How to assign votes in a distributed system
 Journal of the ACM
, 1985
"... Abstract. In a distributed system, one strategy for achieving mutual exclusion of groups of nodes without communication is to assign to each node a number of votes. Only a group with a majority of votes can execute the critical operations, and mutual exclusion is achieved because at any given time t ..."
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Cited by 204 (2 self)
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Abstract. In a distributed system, one strategy for achieving mutual exclusion of groups of nodes without communication is to assign to each node a number of votes. Only a group with a majority of votes can execute the critical operations, and mutual exclusion is achieved because at any given time there is at most one such group. A second strategy, which appears to be similar to votes, is to define a priori a set of groups that intersect each other. Any group of nodes that finds itself in this set can perform the restricted operations. In this paper, both of these strategies are studied in detail and it is shown that they are not equivalent in general (although they are in some cases). In doing so, a number of other interesting properties are proved. These properties will be of use to a system designer who is selecting a vote assignment or a set of groups for a specific application.
Multilevel kway Hypergraph Partitioning
, 1999
"... In this paper, we present a new multilevel kway hypergraph partitioning algorithm that substantially outperforms the existing stateoftheart KPM/LR algorithm for multiway partitioning, both for optimizing local as well as global objectives. Experiments on ..."
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Cited by 168 (11 self)
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In this paper, we present a new multilevel kway hypergraph partitioning algorithm that substantially outperforms the existing stateoftheart KPM/LR algorithm for multiway partitioning, both for optimizing local as well as global objectives. Experiments on
Should Tables Be Sorted?
, 1979
"... We examine optimality questions in the following information retrieval problem: Given a set S of n keys, store them so that queries of the form "Is X \in S?" can be answered quickly. It is shown that, in a rather general model including all the commonlyused schemes, rMn+qi P ro bes to the ..."
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Cited by 160 (0 self)
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We examine optimality questions in the following information retrieval problem: Given a set S of n keys, store them so that queries of the form "Is X \in S?" can be answered quickly. It is shown that, in a rather general model including all the commonlyused schemes, rMn+qi P ro bes to the table are needed in the worst case, provided the key space is sufficiently large. The effects of smaller key space and arbitrary encoding are also explored.
An Incremental Algorithm for a Generalization of the ShortestPath Problem
, 1992
"... The grammar problem, a generalization of the singlesource shortestpath problem introduced by Knuth, is to compute the minimumcost derivation of a terminal string from each nonterminal of a given contextfree grammar, with the cost of a derivation being suitably defined. This problem also subsume ..."
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Cited by 144 (1 self)
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The grammar problem, a generalization of the singlesource shortestpath problem introduced by Knuth, is to compute the minimumcost derivation of a terminal string from each nonterminal of a given contextfree grammar, with the cost of a derivation being suitably defined. This problem also subsumes the problem of finding optimal hyperpaths in directed hypergraphs (under varying optimization criteria) that has received attention recently. In this paper we present an incremental algorithm for a version of the grammar problem. As a special case of this algorithm we obtain an efficient incremental algorithm for the singlesource shortestpath problem with positive edge lengths. The aspect of our work that distinguishes it from other work on the dynamic shortestpath problem is its ability to handle "multiple heterogeneous modifications": between updates, the input graph is allowed to be restructured by an arbitrary mixture of edge insertions, edge deletions, and edgelength changes.
Directed Hypergraphs And Applications
, 1992
"... We deal with directed hypergraphs as a tool to model and solve some classes of problems arising in Operations Research and in Computer Science. Concepts such as connectivity, paths and cuts are defined. An extension of the main duality results to a special class of hypergraphs is presented. Algorith ..."
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Cited by 141 (5 self)
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We deal with directed hypergraphs as a tool to model and solve some classes of problems arising in Operations Research and in Computer Science. Concepts such as connectivity, paths and cuts are defined. An extension of the main duality results to a special class of hypergraphs is presented. Algorithms to perform visits of hypergraphs and to find optimal paths are studied in detail. Some applications arising in propositional logic, AndOr graphs, relational data bases and transportation analysis are presented. January 1990 Revised, October 1992 ( * ) This research has been supported in part by the "Comitato Nazionale Scienza e Tecnologia dell'Informazione", National Research Council of Italy, under Grant n.89.00208.12, and in part by research grants from the National Research Council of Canada. 1 Dipartimento di Informatica, Università di Pisa, Italy 2 Département d'Informatique et de Recherche Opérationnelle, Université de Montréal, Canada 2 INTRODUCTION Hypergraphs, a generaliz...