Packing multiway cuts in capacitated graphs

We consider the following "multiway cut packing" problem in undirected graphs: we are given a graph G=(V,E) and k commodities, each corresponding to a set of terminals located at different vertices in the graph; our goal is to produce a collection of cuts {E_1,...,E_k} such that E_i is a multiway cut for commodity i and the maximum load on any edge is minimized. The load on an edge is defined to be the number of cuts in the solution crossing the edge. In the capacitated version of the problem the goal is to minimize the maximum relative load on any edge--the ratio of the edge's load to its capacity. Multiway cut packing arises in the context of graph labeling problems where we are given a partial labeling of a set of items and a neighborhood structure over them, and, informally, the goal is to complete the labeling in the most consistent way. This problem was introduced by Rabani, Schulman, and Swamy (SODA'08), who developed an O(log n/log log n) approximation for it in general graphs, as well as an improved O(log^2 k) approximation in trees. Here n is the number of nodes in the graph. We present the first constant factor approximation for this problem in arbitrary undirected graphs. Our approach is based on the observation that every instance of the problem admits a near-optimal laminar solution (that is, one in which no pair of cuts cross each other).Comment: The conference version of this paper is to appear at SODA 2009. This is the full versio

Approximation Algorithms for Multiple Sequence Alignment Under a Fixed Evolutionary Tree

. We consider the problem of aligning sequences related by a given evolutionary tree: given a fixed tree with its leaves labeled with sequences, find ancestral sequences to label the internal nodes so as to minimize the total cost of all the edges in the tree. The cost of an edge is the edit distance between the sequences labeling its endpoints. In this paper, we consider the case when the given tree is a regular d-ary tree for some fixed d and provide a d+1 d01 -approximation algorithm for this problem that runs in time O(d(2kn) d +n 2 k 2d ) where k is the number of leaves in the tree and n is the maximum length of any of the sequences labeling the leaves. We also consider a new bottleneck objective in labeling the internal nodes. In this version, we wish to find the labeling of the internal nodes that minimizes the maximum cost of any edge in the tree. For this problem we provide a simple 2ffi + 1-approximation algorithm where ffi is the depth of the given undirected tree def..

Approximation Algorithms for Multiple Sequence Alignment Under a Fixed Evolutionary Tree

We consider the problem of multiple sequence alignment under a fixed evolutionary tree: given a tree whose leaves are labeled by sequences, find ancestral sequences to label its internal nodes so as to minimize the total length of the tree, where the length of an edge is the edit distance between the sequences labeling its endpoints. We present a new polynomial-time approximation algorithm for this problem, and analyze its performance on regular d-ary trees with d a constant. On such a tree, the algorithm finds a solution within a factor d+1 d\Gamma1 of the minimum in O(k d T (d; n) + k 2d n 2 ) time, where k is the number of leaves in the tree, n is the length of the longest sequence labeling a leaf, and T (d; n) is the time to compute a Steiner point for d sequences of length at most n. (A Steiner point for a set S of sequences is a sequence P that minimizes the sum of the edit distances from P to each sequence in S. The time T (d; n) is O(d2 d n d ), given O(ds d+1 )-..

Generalization of predicates with string arguments

Ankara : The Department of Computer Engineering and the Institute of Engineering and Science of Bilkent University, 2002.Thesis (Master's) -- Bilkent University, 2002.Includes bibliographical references leaves 60-63.String/sequence generalization is used in many different areas such as machine learning, example-based machine translation and DNA sequence alignment. In this thesis, a method is proposed to find the generalizations of the predicates with string arguments from the given examples. Trying to learn from examples is a very hard problem in machine learning, since finding the global optimal point to stop generalization is a difficult and time consuming process. All the work done until now is about employing a heuristic to find the best solution. This work is one of them. In this study, some restrictions applied by the SLGG (Specific Least General Generalization) algorithm, which is developed to be used in an example-based machine translation system, are relaxed to find the all possible alignments of two strings. Moreover, a Euclidian distance like scoring mechanism is used to find the most specific generalizations. Some of the generated templates are eliminated by four different selection/filtering approaches to get a good solution set. Finally, the result set is presented as a decision list, which provides the handling of exceptional cases.Canıtezer, GökerM.S