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Finding AlmostSatisfying Assignments
 In Proceedings of the 30th Annual ACM Symposium on Theory of Computing
, 1997
"... Schaefer showed, long ago, that there are, essentially, only three nontrivial classes of conjunctive Boolean formulae (or constraint satisfaction problems) for which satis ability can be decided in polynomial time (assuming P 6= NP ). These three classes are LIN, 2SAT and HORNSAT. LIN is the c ..."
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Cited by 25 (3 self)
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Schaefer showed, long ago, that there are, essentially, only three nontrivial classes of conjunctive Boolean formulae (or constraint satisfaction problems) for which satis ability can be decided in polynomial time (assuming P 6= NP ). These three classes are LIN, 2SAT and HORNSAT. LIN is the constraint satisfaction problem in which all the constraints are linear equations modulo 2. 2SAT is the constraint satisfaction problem in which all the constraints are disjunctions of at most two variables or their negations. HORNSAT is the constraint satisfaction problem in which all the constraints are Horn clauses, i.e., disjunctions containing at most one negated variable.
New algorithms for twolabel point labeling
 IN: PROC. 8TH ANNUAL EUROPEAN SYMP. ON ALGORITHMS
, 2000
"... Given a label shape L and a set of n points in the plane, the 2label pointlabeling problem consists of placing 2n nonintersecting translated copies of L of maximum size such that each point touches two unique copies—its labels. In this paper we give new and simple approximation algorithms for L ..."
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Cited by 8 (3 self)
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Given a label shape L and a set of n points in the plane, the 2label pointlabeling problem consists of placing 2n nonintersecting translated copies of L of maximum size such that each point touches two unique copies—its labels. In this paper we give new and simple approximation algorithms for L an axisparallel square or a circle. For squares we improve the best previously known approximation factor from 1 1 1 to. For circles the improvement from to ≈ 0.513 is less significant, 3 2 2 but the fact that 1 is not best possible is interesting in its own right. 2 For the decision version of the latter problem we have an NPhardness proof that also shows that it is NPhard to approximate the label size beyond a factor of ≈ 0.732. As their predecessors, our algorithms take O(n log n) time and O(n) space.
On Finding Disjoint Paths in Single and Dual Link Cost Networks
, 2004
"... Finding a disjoint path pair is an important component in survivable networks. Since the traffic is carried on the active (working) path most of the time, it is useful to find a disjoint path pair such that the length of the shorter path (to be used as the active path) is minimized. In this paper, w ..."
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Cited by 6 (0 self)
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Finding a disjoint path pair is an important component in survivable networks. Since the traffic is carried on the active (working) path most of the time, it is useful to find a disjoint path pair such that the length of the shorter path (to be used as the active path) is minimized. In this paper, we first address such a MinMin problem. We prove that this problem is NPcomplete in either single link cost (e.g. dedicated backup bandwidth) or dual link cost (e.g. shared backup bandwidth) networks. In addition, it is NPhard to obtain a kapproximation to the optimal solution for any k>1. Our proof is extended to another open question regarding the computational complexity of a restricted version of the MinSum problem in an undirected network with ordered dual cost links (called MSOD problem). To solve the MinMin problem efficiently, we introduce a novel concept called conflicting link set which provides insights into the socalled trap problem, and develop a divideandconquer strategy. The result is an effective heuristic for the MinMin problem called COLE, which can outperform other approaches in terms of both the optimality and running time. We also apply COLE to the MSOD problem to efficiently provide shared path protection and conduct comprehensive performance evaluation as well as comparison of various schemes for shared path protection. We show that COLE not only processes connection requests much faster than existing ILP based approaches but also achieves a good balance among the AP length, bandwidth efficiency and recovery time.
Improving SAT using 2SAT
 In Proceedings of the 25th Australasian Computer Science Conference
, 2002
"... Propositional satisfiability (SAT) is a fundamental problem of immense practical importance. While SAT is NPcomplete when clauses can contain 3 literals or more, the problem can be solved in linear time when the given formula contains only binary clauses (2SAT). Many complete search algorithms for ..."
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Cited by 3 (0 self)
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Propositional satisfiability (SAT) is a fundamental problem of immense practical importance. While SAT is NPcomplete when clauses can contain 3 literals or more, the problem can be solved in linear time when the given formula contains only binary clauses (2SAT). Many complete search algorithms for SAT solving have taken advantage of 2SAT information that occurs in the statement of the problem in order to simplify the solving process, only one that we are aware of uses 2SAT information that arises in the process of the search, as clauses are simplified. There are a number of possibilities for making use of 2SAT information to improve the SAT solving process: maintaining 2SAT satisfiability during search, detecting unit consequences of the 2SAT clauses, and Krom subsumption using 2SAT clauses. In this paper we investigate the tradeoffs of increasing complex 2SAT handling versus the search space reduction and execution time. We give experimental results illustrating that the SAT solver resulting from the best tradeoff is competitive with state of the art DavisPutnam methods, on hard problems involving a substantial 2SAT component.
Simpler Projective Plane Embedding
, 2000
"... A projective plane is equivalent to a disk with antipodal points identified. A graph is projective planar if it can be drawn on the projective plane with no crossing edges. A linear time algorithm for projective planar embedding has been described by Mohar. We provide a new approach that takes O(n ..."
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Cited by 3 (0 self)
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A projective plane is equivalent to a disk with antipodal points identified. A graph is projective planar if it can be drawn on the projective plane with no crossing edges. A linear time algorithm for projective planar embedding has been described by Mohar. We provide a new approach that takes O(n 2 ) time but is much easier to implement. We programmed a variant of this algorithm and used it to computationally verify the known list of all the projective plane obstructions. Key words: graph algorithms, surface embedding, graph embedding, projective plane, forbidden minor, obstruction 1 Background A graph G consists of a set V of vertices and a set E of edges, each of which is associated with an unordered pair of vertices from V . Throughout this paper, n denotes the number of vertices of a graph, and m is the number of edges. A graph is embeddable on a surface M if it can be drawn on M without crossing edges. Archdeacon's survey [2] provides an excellent introduction to topologica...
Consensus List Colorings of Graphs and Physical Mapping of DNA
 Bioconsensus, DIMACS Series, American Mathematical Society, Providence, RI
, 2002
"... In graph coloring, one assigns a color to each vertex of a graph so that neighboring vertices get dierent colors. We shall talk about a bioconsensus problem relating to graph coloring and discuss the applicability of the ideas to the DNA physical mapping problem. In many applications of graph colori ..."
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Cited by 3 (1 self)
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In graph coloring, one assigns a color to each vertex of a graph so that neighboring vertices get dierent colors. We shall talk about a bioconsensus problem relating to graph coloring and discuss the applicability of the ideas to the DNA physical mapping problem. In many applications of graph coloring, one gathers data about the acceptable colors at each vertex. A list coloring is a graph coloring so that the color assigned to each vertex belongs to the list of acceptable colors associated with that vertex. We consider the situation where a list coloring cannot be found. If the data contained in the lists associated with each vertex are made available to individuals associated with the vertices, it is possible that the individuals can modify their lists through trades or exchanges until the group of individuals reaches a set of lists for which a list coloring exists. We describe several models under which such a consensus set of lists might be attained. In the physical mapping application, the lists consist of the sets of possible copies of a target DNA molecule from which a given clone was obtained and trades or exchanges correspond to correcting errors in data.
Speculative Pruning for Boolean Satisfiability
, 1998
"... Much recent work on boolean satisability has focussed on incomplete algorithms that sacrice accuracy for improved running time. Statistical predictors of satisability do not return actual satisfying assignments, but at least two have been developed that run in linear time. Search algorithms all ..."
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Much recent work on boolean satisability has focussed on incomplete algorithms that sacrice accuracy for improved running time. Statistical predictors of satisability do not return actual satisfying assignments, but at least two have been developed that run in linear time. Search algorithms allow increased accuracy with additional running time, and can return satisfying assignments. The ecient search algorithms that have been proposed are based on iteratively improving a random assignment, in eect searching a graph of degree equal to the number of variables. In this paper, we examine an incomplete algorithm based on searching a standard binary tree, in which statistical predictors are used to speculatively prune the tree in constant time. Experimental evaluation on hard random instances shows it to be the rst practical incomplete algorithm based on tree search, surpassing even graphbased methods on smaller instances. 1 Introduction Satisability, determining whe...
Algorithm to solve the problem 2SAT
"... An algorithm to solve the problem #2SAT is shown. We show that the computational time of the presented algorithm is bounded above by a function of order O , where n is the number of the Boolean variables and m is the number of clauses in the instance conjunctive form. Nevertheless, this ..."
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An algorithm to solve the problem #2SAT is shown. We show that the computational time of the presented algorithm is bounded above by a function of order O , where n is the number of the Boolean variables and m is the number of clauses in the instance conjunctive form. Nevertheless, this is a strict upper bound, which can be improved.
Sat Is Solvable In LinearTime
, 1998
"... A lineartime algorithm, with respect to the size of the instance Boolean formula, is presented for the #SAT problem restricted to formulae of the form #2; 2CF, i.e. formulae whose clauses have just two literals and in which each variable appears at most twice. ..."
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A lineartime algorithm, with respect to the size of the instance Boolean formula, is presented for the #SAT problem restricted to formulae of the form #2; 2CF, i.e. formulae whose clauses have just two literals and in which each variable appears at most twice.