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Incompressibility of H-Free Edge Modification Problems

by Leizhen Cai, Yufei Cai , 2014
"... Given a fixed graph H, the H-Free Edge Deletion (resp., Completion, Editing) problem asks whether it is possible to delete from (resp., add to, delete from or add to) the input graph at most k edges so that the resulting graph is H-free, i.e., contains no induced subgraph isomorphic to H. These H-fr ..."
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for H being paths, cycles or 3-connected graphs. We also give a sufficient condition for the nonexistence of polynomial kernels for F-Free Edge Deletion problems, where F is a finite set of forbidden induced subgraphs. As an eective tool, we have introduced an incompressible constraint satis

unknown title

by Leizhen Cai , Yufei Cai , L Cai , Y Cai , Y Cai , 2015
"... Abstract Given a fixed graph H , the H -Free Edge Deletion (resp., Completion, Editing) problem asks whether it is possible to delete from (resp., add to, delete from or add to) the input graph at most k edges so that the resulting graph is H -free, i.e., contains no induced subgraph isomorphic to ..."
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characterize their nonexistence for H being paths, cycles or 3-connected graphs. We also give a sufficient condition for the nonexistence of polynomial kernels for F-Free Edge Deletion problems, where F is a finite set of forbidden induced subgraphs. As an effective tool, we have introduced an incompressible

Fibonacci Heaps and Their Uses in Improved Network optimization algorithms

by Michael L. Fredman, Robert Endre Tarjan , 1987
"... In this paper we develop a new data structure for implementing heaps (priority queues). Our structure, Fibonacci heaps (abbreviated F-heaps), extends the binomial queues proposed by Vuillemin and studied further by Brown. F-heaps support arbitrary deletion from an n-item heap in qlogn) amortized tim ..."
Abstract - Cited by 739 (18 self) - Add to MetaCart
In this paper we develop a new data structure for implementing heaps (priority queues). Our structure, Fibonacci heaps (abbreviated F-heaps), extends the binomial queues proposed by Vuillemin and studied further by Brown. F-heaps support arbitrary deletion from an n-item heap in qlogn) amortized

A Data Structure for Dynamic Trees

by Daniel D. Sleator, Robert Endre Tarjan , 1983
"... A data structure is proposed to maintain a collection of vertex-disjoint trees under a sequence of two kinds of operations: a link operation that combines two trees into one by adding an edge, and a cut operation that divides one tree into two by deleting an edge. Each operation requires O(log n) ti ..."
Abstract - Cited by 347 (21 self) - Add to MetaCart
A data structure is proposed to maintain a collection of vertex-disjoint trees under a sequence of two kinds of operations: a link operation that combines two trees into one by adding an edge, and a cut operation that divides one tree into two by deleting an edge. Each operation requires O(log n

Node- and edge-deletion NP-complete problems

by Mihalis Yannakakis - CONFERENCE RECORD OF THE TENTH ANNUAL ACM SYMPOSIUM ON THEORY OF COMPUTING (SAN DIEGO, CALIF., 1978), ACM , 1978
"... If ~ is a graph property, the general node(edge) deletion problem can be stated as follows: Find the minimum number of nodes(edges), whose deletion results in a subgraph satisfying property ~. In this paper we show that if ~ belongs to a rather broad class of properties (the class of properties that ..."
Abstract - Cited by 95 (0 self) - Add to MetaCart
If ~ is a graph property, the general node(edge) deletion problem can be stated as follows: Find the minimum number of nodes(edges), whose deletion results in a subgraph satisfying property ~. In this paper we show that if ~ belongs to a rather broad class of properties (the class of properties

ON FAIR EDGE DELETION PROBLEMS

by Petr Kolman, Bernard Lidicky, Jean-Sébastien Sereni , 2009
"... In edge deletion problems, we are given a graph G and a graph property π and the task is to find a subset of edges the deletion of which results in a subgraph of G satisfying the property π. Typically the objective is to minimize the total number of deleted edges while in less common fair versions t ..."
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In edge deletion problems, we are given a graph G and a graph property π and the task is to find a subset of edges the deletion of which results in a subgraph of G satisfying the property π. Typically the objective is to minimize the total number of deleted edges while in less common fair versions

Additive approximation for edge-deletion problems

by Noga Alon, Asaf Shapira, Benny Sudakov - Proc. of FOCS 2005 , 2005
"... A graph property is monotone if it is closed under removal of vertices and edges. In this paper we consider the following algorithmic problem, called the edge-deletion problem; given a monotone property P and a graph G, compute the smallest number of edge deletions that are needed in order to turn G ..."
Abstract - Cited by 19 (8 self) - Add to MetaCart
A graph property is monotone if it is closed under removal of vertices and edges. In this paper we consider the following algorithmic problem, called the edge-deletion problem; given a monotone property P and a graph G, compute the smallest number of edge deletions that are needed in order to turn

Vertex-deleted and edge-deleted subgraphs

by J. Lauri , 1992
"... Some classical problems in mathematics are of the following general type. If the structure S ′ is associated with each structure S, does S ′ determine S uniquely? In graph theory we ask what knowledge of the graph short of its full incidence relations is sufficient to determine the graph completely. ..."
Abstract - Cited by 4 (0 self) - Add to MetaCart
Some classical problems in mathematics are of the following general type. If the structure S ′ is associated with each structure S, does S ′ determine S uniquely? In graph theory we ask what knowledge of the graph short of its full incidence relations is sufficient to determine the graph completely

An Incremental Algorithm for a Generalization of the Shortest-Path Problem

by G. Ramalingam, Thomas Reps , 1992
"... The grammar problem, a generalization of the single-source shortest-path problem introduced by Knuth, is to compute the minimum-cost derivation of a terminal string from each non-terminal of a given context-free grammar, with the cost of a derivation being suitably defined. This problem also subsume ..."
Abstract - Cited by 139 (1 self) - Add to MetaCart
The grammar problem, a generalization of the single-source shortest-path problem introduced by Knuth, is to compute the minimum-cost derivation of a terminal string from each non-terminal of a given context-free grammar, with the cost of a derivation being suitably defined. This problem also

On Bayesian Network Approximation by Edge Deletion

by Arthur Choi , Hei Chan , Adnan Darwiche - In UAI , 2005
"... Abstract We consider the problem of deleting edges from a Bayesian network for the purpose of simplifying models in probabilistic inference. In particular, we propose a new method for deleting network edges, which is based on the evidence at hand. We provide some interesting bounds on the KL-diverg ..."
Abstract - Cited by 12 (3 self) - Add to MetaCart
Abstract We consider the problem of deleting edges from a Bayesian network for the purpose of simplifying models in probabilistic inference. In particular, we propose a new method for deleting network edges, which is based on the evidence at hand. We provide some interesting bounds on the KL
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