
Preventing Small (𝐬,𝐭)Cuts by Protecting Edges
We introduce and study Weighted Min (s,t)Cut Prevention, where we are g...
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Multibudgeted directed cuts
We study multibudgeted variants of the classic minimum cut problem and ...
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The complexity of highdimensional cuts
Cut problems form one of the most fundamental classes of problems in alg...
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Formulations for designing robust networks. An application to wind power collection
We are interested in the design of survivable capacitated rooted Steiner...
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Minimum Label st Cut has Large Integrality Gaps
Given a graph G=(V,E) with a label set L = l_1, l_2, ..., l_q, in which ...
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On quasipolynomial multicutmimicking networks and kernelization of multiway cut problems
We show the existence of an exact mimicking network of k^O(log k) edges ...
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Competitive Analysis of MinimumCut Maximum Flow Algorithms in Vision Problems
Rapid advances in image acquisition and storage technology underline the...
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Solving hard cut problems via flowaugmentation
We present a new technique for designing FPT algorithms for graph cut problems in undirected graphs, which we call flow augmentation. Our technique is applicable to problems that can be phrased as a search for an (edge) (s,t)cut of cardinality at most k in an undirected graph G with designated terminals s and t. More precisely, we consider problems where an (unknown) solution is a set Z ⊆ E(G) of size at most k such that (1) in GZ, s and t are in distinct connected components, (2) every edge of Z connects two distinct connected components of GZ, and (3) if we define the set Z_s,t⊆ Z as these edges e ∈ Z for which there exists an (s,t)path P_e with E(P_e) ∩ Z = {e}, then Z_s,t separates s from t. We prove that in this scenario one can in randomized time k^O(1) (V(G)+E(G)) add a number of edges to the graph so that with 2^O(k log k) probability no added edge connects two components of GZ and Z_s,t becomes a minimum cut between s and t. We apply our method to obtain a randomized FPT algorithm for a notorious "hard nut" graph cut problem we call Coupled MinCut. This problem emerges out of the study of FPT algorithms for Min CSP problems, and was unamenable to other techniques for parameterized algorithms in graph cut problems, such as Randomized Contractions, Treewidth Reduction or Shadow Removal. To demonstrate the power of the approach, we consider more generally Min SAT(Γ), parameterized by the solution cost. We show that every problem Min SAT(Γ) is either (1) FPT, (2) W[1]hard, or (3) able to express the soft constraint (u → v), and thereby also the mincut problem in directed graphs. All the W[1]hard cases were known or immediate, and the main new result is an FPT algorithm for a generalization of Coupled MinCut.
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