39 research outputs found
An O(n^2 log^2 n) Time Algorithm for Minmax Regret Minsum Sink on Path Networks
We model evacuation in emergency situations by dynamic flow in a network. We want to minimize the aggregate evacuation time to an evacuation center (called a sink) on a path network with uniform edge capacities. The evacuees are initially located at the vertices, but their precise numbers are unknown, and are given by upper and lower bounds. Under this assumption, we compute a sink location that minimizes the maximum "regret." We present the first sub-cubic time algorithm in n to solve this problem, where n is the number of vertices. Although we cast our problem as evacuation, our result is accurate if the "evacuees" are fluid-like continuous material, but is a good approximation for discrete evacuees
Optimal Embedding of Functions for In-Network Computation: Complexity Analysis and Algorithms
We consider optimal distributed computation of a given function of
distributed data. The input (data) nodes and the sink node that receives the
function form a connected network that is described by an undirected weighted
network graph. The algorithm to compute the given function is described by a
weighted directed acyclic graph and is called the computation graph. An
embedding defines the computation communication sequence that obtains the
function at the sink. Two kinds of optimal embeddings are sought, the embedding
that---(1)~minimizes delay in obtaining function at sink, and (2)~minimizes
cost of one instance of computation of function. This abstraction is motivated
by three applications---in-network computation over sensor networks, operator
placement in distributed databases, and module placement in distributed
computing.
We first show that obtaining minimum-delay and minimum-cost embeddings are
both NP-complete problems and that cost minimization is actually MAX SNP-hard.
Next, we consider specific forms of the computation graph for which polynomial
time solutions are possible. When the computation graph is a tree, a polynomial
time algorithm to obtain the minimum delay embedding is described. Next, for
the case when the function is described by a layered graph we describe an
algorithm that obtains the minimum cost embedding in polynomial time. This
algorithm can also be used to obtain an approximation for delay minimization.
We then consider bounded treewidth computation graphs and give an algorithm to
obtain the minimum cost embedding in polynomial time
Counting and enumerating optimum cut sets for hypergraph -partitioning problems for fixed
We consider the problem of enumerating optimal solutions for two hypergraph
-partitioning problems -- namely, Hypergraph--Cut and
Minmax-Hypergraph--Partition. The input in hypergraph -partitioning
problems is a hypergraph with positive hyperedge costs along with a
fixed positive integer . The goal is to find a partition of into
non-empty parts -- known as a -partition -- so as
to minimize an objective of interest.
1. If the objective of interest is the maximum cut value of the parts, then
the problem is known as Minmax-Hypergraph--Partition. A subset of hyperedges
is a minmax--cut-set if it is the subset of hyperedges crossing an optimum
-partition for Minmax-Hypergraph--Partition.
2. If the objective of interest is the total cost of hyperedges crossing the
-partition, then the problem is known as Hypergraph--Cut. A subset of
hyperedges is a min--cut-set if it is the subset of hyperedges crossing an
optimum -partition for Hypergraph--Cut.
We give the first polynomial bound on the number of minmax--cut-sets and a
polynomial-time algorithm to enumerate all of them in hypergraphs for every
fixed . Our technique is strong enough to also enable an -time
deterministic algorithm to enumerate all min--cut-sets in hypergraphs, thus
improving on the previously known -time deterministic algorithm,
where is the number of vertices and is the size of the hypergraph. The
correctness analysis of our enumeration approach relies on a structural result
that is a strong and unifying generalization of known structural results for
Hypergraph--Cut and Minmax-Hypergraph--Partition. We believe that our
structural result is likely to be of independent interest in the theory of
hypergraphs (and graphs).Comment: Accepted to ICALP'22. arXiv admin note: text overlap with
arXiv:2110.1481
Algorithms for the survivable telecommunications network design problem under dedicated protection
Ankara : The Department of Industrial Engineering and the Institute of Engineering and Sciences of Bilkent University, 2010.Thesis (Master's) -- Bilkent University, 2010.Includes bibliographical references leaves 49-50.This thesis presents algorithms to solve a survivable network design problem arising
in telecommunications networks. As a design problem, we seek to find 2-edge
disjoint paths between every potential origin destination pair such that the fixed
costs of installing edges and the routing costs are jointly minimized. Despite the
fact that the survivable network design literature is vast, the particular problem
at hand incorporating fixed and variable edge costs as well as different cost structures
on the two paths has not been studied. Initially, an IP model addressing the
proposed problem is developed. In order to solve problems of higher dimensions,
different heuristic algorithms are designed and results of a computational study
on a large bed of problem instances are reported.Damcı, PelinM.S
Variants of Shortest Path Problems
The shortest path problem in which the (s, t) -paths P of a given digraph G = (V, E) are compared with respect to the sum of their edge costs is one of the best known problems in combinatorial optimization. The paper is concerned with a number of variations of this problem having different objective functions like bottleneck, balanced, minimum deviation, algebraic sum, k -sum and k -max objectives, (k 1, k 2) -max, (k 1, k 2) -balanced and several types of trimmed-mean objectives. We give a survey on existing algorithms and propose a general model for those problems not yet treated in literature. The latter is based on the solution of resource constrained shortest path problems with equality constraints which can be solved in pseudo-polynomial time if the given graph is acyclic and the number of resources is fixed. In our setting, however, these problems can be solved in strongly polynomial time. Combining this with known results on k -sum and k -max optimization for general combinatorial problems, we obtain strongly polynomial algorithms for a variety of path problems on acyclic and general digraphs
Scheduling with Communication Delays
International audiencehanbook on ordonnancemen