Results 1  10
of
10
Formal Language Constrained Path Problems
, 1998
"... Given an alphabet Sigma, a (directed) graph G whose edges are weighted and Sigmalabeled, and a formal language L , the Formal Language Constrained Shortest/Simple Path problem consists of finding a shortest (simple) path p in G complying with the additional constraint that l(p) 2 L. Here l(p) denot ..."
Abstract

Cited by 17 (9 self)
 Add to MetaCart
Given an alphabet Sigma, a (directed) graph G whose edges are weighted and Sigmalabeled, and a formal language L , the Formal Language Constrained Shortest/Simple Path problem consists of finding a shortest (simple) path p in G complying with the additional constraint that l(p) 2 L. Here l(p) denotes the unique word given by concatenating the Sigmalabels of the edges along the path p. The main contributions of this paper include the following: 1. We show that the formal language constrained shortest path problem is solvable efficiently in polynomial time when L is restricted to be a context free language. When L is specified as a regular language we provide algorithms with improved space and time bounds...
Modifying Edges of a Network to Obtain Short Subgroups
, 1996
"... This paper considers problems of the following type: We are given an edge weighted graph G = (V, E). It is assumed that each edge e of the given network has an associated function c_e that specifies the cost of shortening the edge by a given amount and that there is a budget B on the total reduction ..."
Abstract

Cited by 12 (2 self)
 Add to MetaCart
This paper considers problems of the following type: We are given an edge weighted graph G = (V, E). It is assumed that each edge e of the given network has an associated function c_e that specifies the cost of shortening the edge by a given amount and that there is a budget B on the total reduction cost. The goal is to develop a reduction strategy satisfying the budget constraint so that the total length of a minimum spanning tree in the modified network is the smallest possible over all reduction strategies that obey the budget constraint. We show that in general the problem of computing an optimal reduction strategy for modifying the network as above is NPhard even for simple classes of graphs and linear functions c_e. We present the first polynomial time approximation algorithms for the problem, where the cost functions c_e are allowed to be taken from a broad class of functions. We also present improved approximation algorithms for the class of treewidthbounded graphs when the cost functions are linear...
Approximation khop minimumspanning trees
, 2004
"... Given a complete graph on n nodes with metric edge costs, the minimumcost k hop spanning tree (kHMST) problem asks for a spanning tree of minimum total cost such that the longest rootleafpath in the tree has at most k edges. We present an algorithm that computes such a tree of total expected co ..."
Abstract

Cited by 12 (0 self)
 Add to MetaCart
Given a complete graph on n nodes with metric edge costs, the minimumcost k hop spanning tree (kHMST) problem asks for a spanning tree of minimum total cost such that the longest rootleafpath in the tree has at most k edges. We present an algorithm that computes such a tree of total expected cost O(log n) times that of a minimumcost khop spanningtree.
Budgeted matching and budgeted matroid intersection via the gasoline puzzle
 IN PROC. IPCO 2008
, 2008
"... Many polynomialtime solvable combinatorial optimization problems become NPhard if an additional complicating constraint is added to restrict the set of feasible solutions. In this paper, we consider two such problems, namely maximumweight matching and maximumweight matroid intersection with on ..."
Abstract

Cited by 9 (1 self)
 Add to MetaCart
Many polynomialtime solvable combinatorial optimization problems become NPhard if an additional complicating constraint is added to restrict the set of feasible solutions. In this paper, we consider two such problems, namely maximumweight matching and maximumweight matroid intersection with one additional budget constraint. We present the first polynomialtime approximation schemes for these problems. Similarly to other approaches for related problems, our schemes compute two solutions to the Lagrangian relaxation of the problem and patch them together to obtain a nearoptimal solution. However, due to the richer combinatorial structure of the problems considered here, standard patching techniques do not apply. To circumvent this problem, we crucially exploit the adjacency relations on the solution polytope and, surprisingly, the solution to an old combinatorial puzzle.
Computing A DiameterConstrained Minimum Spanning Tree
, 2001
"... In numerous practical applications, it is necessary to find the smallest possible tree with a bounded diameter. A diameterconstrained minimum spanning tree (DCMST) of a given undirected, edgeweighted graph, G, is the smallestweight spanning tree of all spanning trees of G which contain no path wi ..."
Abstract

Cited by 8 (0 self)
 Add to MetaCart
In numerous practical applications, it is necessary to find the smallest possible tree with a bounded diameter. A diameterconstrained minimum spanning tree (DCMST) of a given undirected, edgeweighted graph, G, is the smallestweight spanning tree of all spanning trees of G which contain no path with more than k edges, where k is a given positive integer. The problem of finding a DCMST is NPcomplete for all values of k; 4 k (n  2), except when all edgeweights are identical. A DCMST is essential for the efficiency of various distributed mutual exclusion algorithms, where it can minimize the number of messages communicated among processors per critical section. It is also useful in linear lightwave networks, where it can minimize interference in the network by limiting the traffic in the network lines. Another practical application requiring a DCMST arises in data compression, where some algorithms compress a file utilizing a tree datastructure, and decompress a path in the tree to access a record. A DCMST helps such algorithms to be fast without sacrificing a lot of storage space. We present a survey of the literature on the DCMST problem, study the expected diameter of a random labeled tree, and present five new polynomialtime algorithms for an approximate DCMST. One of our new algorithms constructs an approximate DCMST in a modified greedy fashion, employing a heuristic for selecting an edge to be added to iii the tree in each stage of the construction. Three other new algorithms start with an unconstrained minimum spanning tree, and iteratively refine it into an approximate DCMST. We also present an algorithm designed for the special case when the diameter is required to be no more than 4. Such a diameter4 tree is also used for evaluating the quality of o...
Approximation Algorithms for Certain Network Improvement Problems
 J. Comb. Optim
, 1998
"... . We study budget constrained network upgrading problems. Such problems aim at nding optimal strategies for improving a network under some cost measure subject to certain budget constraints. Given an edge weighted graph G = (V; E), in the edge based upgrading model, it is assumed that each edge e of ..."
Abstract

Cited by 8 (0 self)
 Add to MetaCart
. We study budget constrained network upgrading problems. Such problems aim at nding optimal strategies for improving a network under some cost measure subject to certain budget constraints. Given an edge weighted graph G = (V; E), in the edge based upgrading model, it is assumed that each edge e of the given network also has an associated function ce (t) that species the cost of upgrading the edge by an amount t. A reduction strategy species for each edge e the amount by which the length `(e) is to be reduced. In the node based upgrading model, a node v can be upgraded at an expense of c(v). Such an upgrade reduces the delay of each edge incident on v. For a given budget B, the goal is to nd an improvement strategy such that the total cost of reduction is at most the given budget B and the cost of a subgraph (e.g. minimum spanning tree) under the modied edge lengths is the best over all possible strategies which obey the budget constraint. After providing a brief overview of the...
Budget Constrained Minimum Cost Connected Medians
"... Several practical instances of network design and location theory problems require the network to satisfy multiple constraints. In this paper, we study a graphtheoretic problem that aims to simultaneously address a network design task and a locationtheoretic constraint. The Budget Constrained Conn ..."
Abstract

Cited by 1 (0 self)
 Add to MetaCart
Several practical instances of network design and location theory problems require the network to satisfy multiple constraints. In this paper, we study a graphtheoretic problem that aims to simultaneously address a network design task and a locationtheoretic constraint. The Budget Constrained Connected Median Problem is the following: We are given an undirected graph G = (V; E) with two different edgeweight functions c (modeling the construction or communication cost) and d (modeling the service distance), and a bound B on the total service distance. The goal is to find a subtree T of G with minimum ccost c(T ) subject to the constraint that the sum v2V nT dist d (v; T ) of the service distances of all the remaining nodes v 2 V n T does not exceed the specified budget B. Here, the service distance dist d (v; T ) denotes the shortest path distance of v to a vertex in T with respect to d. This problem has applications in optical network design and the efficient maintenance of distributed databases.
Steiner ShallowLight Trees are Exponentially Lighter than Spanning Ones
"... Abstract — For a pair of parameters α, β ≥ 1, a spanning tree T of a weighted undirected nvertex graph G =(V,E,w) is called an (α, β)shallowlight tree (shortly, (α, β)SLT) of G with respect to a designated vertex rt ∈ V if (1) it approximates all distances from rt to the other vertices up to a f ..."
Abstract

Cited by 1 (0 self)
 Add to MetaCart
Abstract — For a pair of parameters α, β ≥ 1, a spanning tree T of a weighted undirected nvertex graph G =(V,E,w) is called an (α, β)shallowlight tree (shortly, (α, β)SLT) of G with respect to a designated vertex rt ∈ V if (1) it approximates all distances from rt to the other vertices up to a factor of α, and (2) its weight is at most β times the weight of the minimum spanning tree MST(G) of G. The parameter α (respectively, β) is called the rootdistortion (resp., lightness) ofthetreeT. Shallowlight trees (SLTs) constitute a fundamental graph structure, with numerous theoretical and practical applications. In particular, they were used for constructing spanners, in network design, for VLSIcircuit design, for various data gathering and dissemination tasks in wireless and sensor networks, in overlay networks, and in the messagepassing model of distributed computing. Tight tradeoffs between the parameters of SLTs were established by Awerbuch et al. [5], [6] and Khuller et al. [33]. They showed that for any ɛ>0 there always exist (1 + ɛ, O ( 1))SLTs, and that ɛ the upper bound β = O ( 1) on the lightness of SLTs cannot be ɛ improved. In this paper we show that using Steiner points one can build SLTs with logarithmic lightness, i.e., β = O(log 1 ɛ).This establishes an exponential separation between spanning SLTs and Steiner ones. One particularly remarkable point on our tradeoff curve is ɛ = 0. In this regime our construction provides a shortestpath tree with weight at most O(log n) · w(MST(G)). Moreover, we prove matching lower bounds that show that all our results are tight up to constant factors. Finally, on our way to these results we settle (up to constant factors) a number of open questions that were raised by Khuller et al. [33] in SODA’93. Keywordsminimum spanning tree; shortestpath tree; Steiner
Broadcasting Time cannot be Approximated within a Factor of ...
, 2000
"... . In the beginning the information is available only at some sources of a given network. The aim is to inform all nodes of the given network. Therefore, every node can inform its neighborhood sequentially and newly informed nodes can proceed in parallel within their neighborhoods. The process of in ..."
Abstract
 Add to MetaCart
. In the beginning the information is available only at some sources of a given network. The aim is to inform all nodes of the given network. Therefore, every node can inform its neighborhood sequentially and newly informed nodes can proceed in parallel within their neighborhoods. The process of informing one node needs one time unit. The broadcasting problem is to compute the minimum length of such a broadcasting schedule. The computational complexity of broadcasting is investigated and for the first time a constant lower inapproximability bound is stated, i.e. it is NPhard to distinguish between graphs with broadcasting time smaller than b and larger than ( 57 56 \Gamma ffl)b for any ffl ? 0. This improves on the lower bounds known for multiple and single source broadcasting, which could only state that it is NPhard to distinguish between graphs with broadcasting time b and b + 1, for any b 3. This statement is proven by reduction from E3SAT, the analysis of which needs a ca...