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## Publications

Publications (174)

What approximation ratio can we achieve for the Facility Location problem if whenever a client u connects to a facility v, the opening cost of v is at most θ times the service cost of u? We show that this and many other problems are a particular case of the Activation Edge-Cover problem. Here we are given a multigraph G=(V,E), a set R⊆V of terminal...

Directed Steiner Tree (DST) is a central problem in combinatorial optimization and theoretical computer science: Given a directed graph G=(V,E) with edge costs c∈R≥0E, a root r∈V and k terminals K⊆V, we need to output the minimum-cost arborescence in G that contains an r→t path for every t∈K. Recently, Grandoni, Laekhanukit and Li, and independentl...

The DB-GST problem is given an undirected graph G(V,E), and a collection of groups S={Si}i=1q,Si⊆V, find a tree that contains at least one vertex from every group Si, so that the maximum degree is minimal. This problem was motivated by On-Line algorithms Hajiaghayi (2016), and has applications in VLSI design and fast Broadcasting. In the WDB-GST pr...

We introduce the problem of finding a spanning tree along with a partition of the tree edges into the fewest number of feasible sets, where constraints on the edges define feasibility. The motivation comes from wireless networking, where we seek to model the irregularities seen in actual wireless environments. Not all node pairs may be able to comm...

We show that Set-Cover on instances with N elements cannot be approximated within (1-γ)lnN-factor in time exp(Nγ-δ), for any 00, assuming the Exponential Time Hypothesis. This essentially matches the best upper bound known by Cygan, Kowalik, and Wykurz [6] of (1-γ)lnN-factor in time exp(O(Nγ)). The lower bound is obtained by extracting a standalone...

We show that Set Cover on instances with $N$ elements cannot be approximated within $(1-\gamma)\ln N$-factor in time exp($N^{\gamma-\delta})$, for any $0 < \gamma < 1$ and any $\delta > 0$, assuming the Exponential Time Hypothesis. This essentially matches the best upper bound known by Cygan et al.\ (IPL, 2009) of $(1-\gamma)\ln N$-factor in time $...

We consider the aggregation problem in radio networks: find a spanning tree in a given graph and a conflict-free schedule of the edges so as to minimize the latency of the computation. While a large body of literature exists on this and related problems, we give the first approximation results in graphs that are not induced by unit ranges in the pl...

Motivated by some open problems posed in [13], we study three problems that seek a low degree subtree T of a graph \(G=(V,E)\). In the Min-Degree Group Steiner Tree problem we are given a collection of node subsets (groups), and T should contain a node from every group. In the Min-Degree Steiner k-Tree problem we are given a set R of terminals and...

An instance of the Connected Maximum Cut problem consists of an undirected graph G=(V,E) and the goal is to find a subset of vertices S⊆V that maximizes the number of edges in the cut δ(S) such that the induced graph G[S] is connected. We present the first non-trivial Ω(1logn) approximation algorithm for the Connected Maximum Cut problem in genera...

We study two problems that seek a subtree $T$ of a graph $G=(V,E)$ such that $T$ satisfies a certain property and has minimal maximum degree. - In the Min-Degree Group Steiner Tree problem we are given a collection ${\cal S}$ of groups (subsets of $V$) and $T$ should contain a node from every group. - In the Min-Degree Steiner $k$-Tree problem we a...

Given an undirected graph with edge costs, the power of a node is the maximum cost of an edge incident to it, and the power of a graph is the sum of the powers of its nodes. Motivated by applications in wireless networks, we consider two network design problems under the power minimization criteria. In both problems we are given a graph G=(V,E) wit...

This paper concerns proving almost tight (super-polynomial) running times, for achieving desired approximation ratios for various problems. To illustrate, the question we study, let us consider the Set-Cover problem with n elements and m sets. Now we specify our goal to approximate Set-Cover to a factor of (1-d)ln n, for a given parameter 0<d<1. Wh...

Given an undirected graph with edge costs, the power of a node is the maximum cost of an edge incident to it, and the power of a graph is the sum of the powers of its nodes. Motivated by applications in wireless networks, we consider two network design problems under the power minimization criteria. In both problems we are given a graph \(G=(V,E)\)...

We introduce the problem of finding a spanning tree along with a partition of the tree edges into fewest number of feasible sets, where constraints on the edges define feasibility. The motivation comes from wireless networking, where we seek to model the irregularities seen in actual wireless environments. Not all node pairs may be able to communic...

In this paper, we introduce and study the notion of low risk mechanisms. Intuitively, we say a mechanism is a low risk mechanism if the randomization of the mechanism does not affect the utility of agents by a lot. Specifically, we desire to design mechanisms in which the variances of the utility of agents are small. Inspired by this work, later, P...

In the Tree Augmentation problem the goal is to augment a tree T by a minimum size edge set F from a given edge set E such that T F is 2-edge-connected. The best approximation ratio known for the problem is 1.5. In the more general Weighted Tree Augmentation problem, F should be of minimum weight. Weighted Tree Augmentation admits several 2-approxi...

We consider questions that arise from the intersection between the areas of polynomial-time approximation algorithms, subexponential-time algorithms, and fixed-parameter tractable algorithms. The questions, which have been asked several times (e.g., [Marx08, FGMS12, DF13]), are whether there is a non-trivial FPT-approximation algorithm for the Maxi...

In the Steiner k-Forest problem, we are given an edge weighted graph, a collection D of node pairs, and an integer k ⩽ |D|. The goal is to find a min-weight subgraph that connects at least k pairs. The best known ratio for this problem is min {O(&sqrt;n), O(&sqrt;k)} [Gupta et al. 2010]. In Gupta et al. [2010], it is...

In an instance of the (directed) Max Leaf Tree (MLT) problem we are given a vertex-weighted (di)graph G(V,E,w) and the goal is to compute a subtree with maximum weight on the leaves. The weighted Connected Max Cut (CMC) problem takes in an undirected edge-weighted graph G(V,E,w) and seeks a subset S⊆V such that the induced graph G[S] is connected a...

The study of Dense-$3$-Subhypergraph problem was initiated in Chlamt{\'{a}}c et al. [Approx'16]. The input is a universe $U$ and collection ${\cal S}$ of subsets of $U$, each of size $3$, and a number $k$. The goal is to choose a set $W$ of $k$ elements from the universe, and maximize the number of sets, $S\in {\cal S}$ so that $S\subseteq W$. The...

Given an edge-weighted directed graph G = (V, E) on n vertices and a set T = {t(1), t(2), ... , t(p)} of p terminals, the objective of the STRONGLY CONNECTED STEINER SUBGRAPH (p-SCSS) problem is to find an edge set H subset of E of minimum weight such that G[H] contains an t(i) -> t(j) path for each 1 <= i not equal j <= p. The p-SCSS problem is NP...

In Source Location (SL) problems the goal is to select a minimum cost source set S⊆V such that the connectivity (or flow) ψ(S,v) from S to any node v is at least the demand dv of v. In many SL problems ψ(S,v)=dv if v∈S, so the demand of nodes selected to S is completely satisfied. In a variant suggested recently by Fukunaga , every node v selected...

We study the following basic problem called Bi-Covering. Given a graph G(V;E), find two (not necessarily disjoint) sets A ⊆ V and B ⊆ V such that A [ B = V and such that every edge e belongs to either the graph induced by A or the graph induced by B. The goal is to minimize maxfjAj; jBjg. This is the most simple case of the Channel Allocation probl...

In Source Location (SL) problems the goal is to select a minimum cost source set \(S \subseteq V\) such that the connectivity (or flow) \(\psi (S,v)\) from S to any node v is at least the demand \(d_v\) of v. In many SL problems \(\psi (S,v)=d_v\) if \(v \in S\), so the demand of nodes selected to S is completely satisfied. In a variant suggested r...

In the Movement Repairmen (MR) problem, we are given a metric space (V, d) along with a set R of k repairmen r1 , r2,..., rk with their start depots s1 , s2,..., sk ∈ V and speeds v1, v2,... ,vk ≥ 0, respectively, and a set C of m clients c1, c2,..., cm having start locations s1′, s2′,..., sm′ ∈ V and speeds v1′, v2′,..., vm′ ≥ 0, respectively. If...

It was recently found that there are very close connections between the existence of additive spanners (subgraphs where all distances are preserved up to an additive stretch), distance preservers (subgraphs in which demand pairs have their distance preserved exactly), and pairwise spanners (subgraphs in which demand pairs have their distance preser...

The Densest $k$-Subgraph (D$k$S) problem, and its corresponding minimization problem Smallest $p$-Edge Subgraph (S$p$ES), have come to play a central role in approximation algorithms. This is due both to their practical importance, and their usefulness as a tool for solving and establishing approximation bounds for other problems. These two problem...

In this paper we consider the pairwise kidney exchange game. This game naturally appears in situations that some service providers benefit from pairwise allocations on a network, such as the kidney exchanges between hospitals. Ashlagi et al. [1] present a 2-approximation randomized truthful mechanism for this problem. This is the best known result...

We consider the aggregation problem in radio networks: find a spanning tree in a given graph and a conflict-free schedule of the edges so as to minimize the latency of the computation. While a large body of literature exists on this and related problems, we give the first approximation results in graphs that are not induced by unit ranges in the pl...

In the Tree Augmentation Problem (TAP) the goal is to augment a tree $T$ by a
minimum size edge set $F$ from a given edge set $E$ such that $T \cup F$ is
$2$-edge-connected. The best approximation ratio known for TAP is $1.5$. In the
more general Weighted TAP problem, $F$ should be of minimum weight. Weighted
TAP admits several $2$-approximation al...

In this paper we consider the pairwise kidney exchange game. This game
naturally appears in situations that some service providers benefit from
pairwise allocations on a network, such as the kidney exchanges between
hospitals.
Ashlagi et al. present a $2$-approximation randomized truthful mechanism for
this problem. This is the best known result in...

An instance of the Connected Maximum Cut problem consists of an undirected
graph G = (V, E) and the goal is to find a subset of vertices S $\subseteq$ V
that maximizes the number of edges in the cut \delta(S) such that the induced
graph G[S] is connected. We present the first non-trivial \Omega(1/log n)
approximation algorithm for the connected max...

We study two problems related to the Small Set Expansion Conjecture [14]: the Maximum weight
\(m'\)
-edge cover (MWEC) problem and the Fixed cost minimum edge cover (FCEC) problem. In the MWEC problem, we are given an undirected simple graph \(G=(V,E)\) with integral vertex weights. The goal is to select a set \(U\subseteq V\) of maximum weight so...

Given an edge-weighted directed graph \(G=(V,E)\) on \(n\) vertices and a set \(T=\{t_1, t_2, \ldots t_p\}\) of \(p\) terminals, the objective of the Strongly Connected Steiner Subgraph (SCSS) problem is to find an edge set \(H\subseteq E\) of minimum weight such that \(G[H]\) contains a \(t_{i}\rightarrow t_j\) path for each \(1\le i\ne j\le p\)....

In the Fixed Cost
k
-Flow problem, we are given a graph G = (V,E) with edge-capacities {u
e
|e ∈ E} and edge-costs {c
e
|e ∈ E}, source-sink pair s,t ∈ V, and an integer k. The goal is to find a minimum cost subgraph H of G such that the minimum capacity of an st-cut in H is at least k. We show that Group Steiner is a special case of Fixed Cost
k
-...

In this paper, we consider proving inapproximability in terms of OPT and thus
we base the foundations of fixed parameter inapproximability.

In this paper, we consider proving inapproximability in terms of OPT and
thus we base the foundations of fixed parameter inapproximability.

In Gandhi et al. [2006], we gave an algorithm for the data migration and non-deterministic open shop scheduling problems in the minimum sum version, that was claimed to achieve a 5.06-approximation. Unfortunately, it was pointed to us by Maxim Sviridenko that the argument contained an unfounded assumption that has eluded all of its readers until no...

A Fixed-Parameter Tractable (FPT) ρ-approximation algorithm for a minimization (resp. maximization) parameterized problem P is an FPT algorithm that, given an instance (x, k) ∈ P computes a solution of cost at most k ·ρ(k) (resp. k/ρ(k)) if a solution of cost at most (resp. at least) k exists; otherwise the output can be arbitrary. For well-known i...

We study several network design problems with degree constraints. For the minimum-cost Degree-Constrained 2-Node-Connected Subgraph problem, we obtain the first non-trivial bicriteria approximation algorithm, with 5b(v)+35b(v)+3 violation for the degrees and a 4-approximation for the cost. This improves upon the logarithmic degree violation and no...

In the {\em Movement Repairmen (MR)} problem we are given a metric space $(V,
d)$ along with a set $R$ of $k$ repairmen $r_1, r_2, ..., r_k$ with their start
depots $s_1, s_2, ..., s_k \in V$ and speeds $v_1, v_2, ..., v_k \geq 0$
respectively and a set $C$ of $m$ clients $c_1, c_2, ..., c_m$ having start
locations $s'_1, s'_2, ..., s'_m \in V$ and...

Graph clustering is an important problem with applications to bioinformatics, community discovery in social networks, distributed computing, and more. While most of the research in this area has focused on clustering using disjoint clusters, many real datasets have inherently overlapping clusters. We compare overlapping and non-overlapping clusteri...

We consider the k-Directed Steiner Forest (k-DSF) problem: Given a directed graph G=(V,E)G=(V,E) with edge costs, a collection D⊆V×VD⊆V×V of ordered node pairs, and an integer k⩽|D|k⩽|D|, find a minimum cost subgraph H of G that contains an st-path for (at least) k pairs (s,t)∈D(s,t)∈D. When k=|D|k=|D|, we get the Directed Steiner Forest (DSF) prob...

In this paper, we initiate the study of designing approximation algorithms for Fault- Tolerant Group-Steiner (FTGS) problems. The motivation is to protect the well-studied group-Steiner networks from edge or vertex failures. In Fault-Tolerant Group-Steiner prob- lems, we are given a graph with edge- (or vertex-) costs, a root vertex, and a collecti...

We consider connectivity problems with orientation constraints. Given a directed graph D and a collection of ordered node pairs P let P[D] = {(u,v) ∈ P: D contains a uv− path}. In the Steiner Forest Orientation problem we are given an undirected graph G = (V,E) with edge-costs and a set P ⊆ V ×V of ordered node pairs. The goal is to find a minimum-...

We focus on designing combinatorial algorithms for the Capacitated Network
Design problem (Cap-SNDP). The Cap-SNDP is the problem of satisfying
connectivity requirements when edges have costs and hard capacities. We begin
by showing that the Group Steiner tree problem (GST) is a special case of
Cap-SNDP even when there is connectivity requirement b...

We consider the scheduling of biprocessor jobs under sum objective (BPSMSM). Given a collection of unit-length jobs where each job requires the use of two processors, find a schedule such that no two jobs involving the same processor run concurrently. The objective is to minimize the sum of the completion times of the jobs. Equivalently, we would l...

The Tree Augmentation Problem (TAP) is: given a connected graph $G=(V,{\cal
E})$ and an edge set $E$ on $V$ find a minimum size subset of edges $F
\subseteq E$ such that $(V,{\cal E} \cup F)$ is $2$-edge-connected. In the
conference version \cite{EFKN-APPROX} was sketched a $1.5$-approximation
algorithm for the problem. Since a full proof was very...

We study a very natural local protocol for a file transfer problem. Consider a scenario where several files, which may have varied sizes and get created over a period of time, are to be transferred between pairs of hosts in a distributed environment. Our protocol assumes that while executing the file transfers, an individual host does not use any g...

We study several network design problems with degree constraints. For the degree-constrained 2-connected subgraph problem
we obtain a factor 6 violation for the degrees with 4 approximation for the cost. This improves upon the logarithmic degree
violation and no cost guarantee obtained by Feder, Motwani, and Zhu (2006). Then we consider the problem...

In this paper we consider the checkpoint problem. The input consists of an undirected graph G, a set of source-destination pairs {(s
1,t
1), ...,(s
k
,t
k
)}, and a collection P{\cal P} of paths connecting the (s
i
,t
i
) pairs. A feasible solution is a multicut E′; namely, a set of edges whose removal disconnects every source-destination pair....

In a Content Distribution Network application, we have a set of servers and a set of clients to be connected to the servers. Often there are a few server types and a hard budget constraint on the number of deployed servers of each type. The simplest goal here is to deploy a set of servers subject to these budget constraints in order to minimize the...

In the Steiner Network problem we are given a graph G with edge-costs and connectivity requirements r
uv
between node pairs u,v. The goal is to find a minimum-cost subgraph H of G that contains r
uv
edge-disjoint paths for all u,v ∈ V. In Prize-Collecting Steiner Network problems we do not need to satisfy all requirements, but are given a penalty f...

Buy-at-bulk network design problems arise in settings where the costs for purchasing or installing equipment exhibit economies of scale. The objective is to build a network of cheapest cost to support a given multicommodity flow demand between node pairs. We present approximation algorithms for buy-at-bulk network design problems with costs on both...

We study several multi-criteria undirected network design problems with node costs and lengths with all problems related to the node costs Multicommodity Buy at Bulk (mbb) problem in which we are given a graph G = (V,E), demands {d
st
: s,t ∈ V}, and a family {c
v
: v ∈ V} of subadditive cost functions. For every s,t ∈ V we seek to send d
st
flow u...

Given a graph with edge costs, the power of a node is the maximum cost of an edge leaving it, and the power of a graph is the sum of the powers of its nodes. Motivated by applications in wireless networks, we consider several fundamental undirected network design problems under the power minimization criteria. The Minimum-Power Edge-Cover (MPEC) pr...

We present a 1.8-approximation algorithm for the following NP-hard problem: given a con- nected graph G = (V, E) and an additional edge set E, find a minimum size subset of edges F ⊆ E such that (V, E ∪ F) is 2-edge-connected. Our result improves and simplifies the approx- imation algorithm of ratio 1.875 + ε (17).

We consider the k-Directed Steiner Forest (k-DSF) problem: given a directed graph G = (V, E) with edge costs, a collection D ⊆ V x V of ordered node pairs, and an integer k ≤ |D|, find a min-cost subgraph H of G that contains an st-path for (at least) kc pairs (s, t) ∈ D. When k = |D|, we get the Directed Steiner Forest (DSF) problem. The best know...

In this paper, we initiate the study of designing approximation algorithms for Fault-Tolerant Group-Steiner (FIGS) problems. The motivation is to protect the well-studied group-Steiner networks from edge or vertex failures. In Fault-Tolerant Group-Steiner problems, we are given a graph with edge- (or vertex-) costs, a root vertex, and a collection...

We study two-stage robust variants of combinatorial optimization problems like Steiner tree, Steiner forest, and uncapacitated facility location. The robust optimization problems, previously studied by Dhamdhere et al. [1], Golovin et al. [6], and Feige et al. [4], are two-stage planning problems in which the requirements are revealed after some de...

We consider Source Location (SL) problems: given a capacitated network G=(V,E), cost c(v) and a demand d(v) for every v∈V, choose a min-cost S⊆V so that λ(v,S)⩾d(v) holds for every v∈V, where λ(v,S) is the maximum flow value from v to S. In the directed variant, we have demands din(v) and dout(v) and we require λ(S,v)⩾din(v) and λ(v,S)⩾dout(v). Und...

We study approximation algorithms, integrality gaps, and hardness of approximation, of two problems related to cycles of “small”
length k in a given graph. The instance for these problems is a graph G = (V,E) and an integer k. The k
-Cycle Transversal problem is to find a minimum edge subset of E that intersects every k-cycle. The k
-Cycle-Free Sub...

We consider the scheduling of biprocessor jobs under sum objective (BPSMS). Given a collection of unit-length jobs where each job requires the use of two processors, find a schedule such that no two jobs involving the same processor run concurrently. The objective is to minimize the sum of the completion times of the jobs. Equivalently, we would li...

Power optimization is a central issue in wireless network design. Given a graph with costs on the edges, the power of a node
is the maximum cost of an edge incident to it, and the power of a graph is the sum of the powers of its nodes. Motivated by
applications in wireless networks, we consider several fundamental undirected network design problems...

We consider a general class of scheduling problems where a set of conflicting jobs needs to be scheduled (preemptively or nonpreemptively) on a set of machines so as to minimize the weighted sum of completion times. The conflicts among jobs are formed as an arbitrary conflict graph.
Building on the framework of Queyranne and Sviridenko [2002b], we...

A complete partition of a graph G is a partition of its vertex set in which any two distinct classes are connected by an edge. Let cp(G) denote the maximum number of classes in a complete partition of G. This measure was defined in 1969 by Gupta [19], and is known to be NP-hard to compute for several classes of graphs. We obtain essentially tight l...

The min-Shift Design problem (MSD) is an important scheduling problem that needs to be solved in many industrial contexts. The issue is to find a minimum number
of shifts and the number of employees to be assigned to these shifts in order to minimize the deviation from workforce requirements.
Our research considers both theoretical and practical a...

Given a graph with costs on the edges, the power of a node is the maximum cost of an edge leaving it, and the power of the
graph is the sum of the powers of the nodes of this graph. Motivated by applications in wireless multi-hop networks, we consider
four fundamental problems under the power minimization criteria: the Min-Power b-Edge-Cover proble...

We show that for every radio network G = ( V , E ) and source s ∈ V , there exists a radio broadcast schedule for G of length Rad ( G , s ) + O (√ Rad ( G , s ) ⋅log ² n ) = O ( Rad ( G , s ) + log ⁴ n ), where Rad ( G , s ) is the radius of the radio network G with respect to the source s . This result improves the previously best-known upper boun...

We present an Ω(log2k) lower bound on the integrality ratio of the flow-based relaxation for the Group Steiner Tree problem, where k denotes the number of groups; this holds even for input graphs that are Hierarchically Well-Separated Trees, introduced by Bartal [Symp. Foundations of Computer Science, pp. 184--193, 1996], in which case this lower b...

We present algorithms with poly-logarithmic approximation ratios for the buy-at-bulk network design problem in the node-weighted setting. We obtain the following results where h is the number of pairs in the input. • An O(log h) approximation for the single-sink non-uniform buy-at-bulk network design. Unless P = N P this ratio is tight up to consta...

We study two related network design problems with two cost functions. In the buy-at-bulk k-Steiner tree problem we are given a graph G(V,E) with a set of terminals T⊆V including a particular vertex s called the root, and an integer k≤|T|. There are two cost functions on the edges of G, a buy cost b:E→ℝ+ and a distance cost r:E→ℝ+. The goal is to fi...

Consider a network of processors modeled by an n-vertex directed graph G = (V,E). Assume that the communication in the network
is synchronous, i.e., occurs in discrete "rounds," and in every round every processor is allowed to pick one of its neighbors,
and to send him a message. A set of terminals T ⫅ V of size |T| = k is given. The telephone k-mu...

The S-connectivity
λ
S
G
(u,v) of (u,v) in a graph G is the maximum number of uv-paths that no two of them have an edge or a node in S–{u,v} in common. The corresponding Connectivity Augmentation (CA) problem is: given a graph G
0=(V,E
0), S ⊆ V, and requirements r(u,v) on V ×V, find a minimum size set F of new edges (any edge is allowed) so that \...

Consider a network of processors modeled by an n-vertex graph . Assume that the communication in the network is synchronous, i.e., occurs in discrete “rounds,” and in every round every processor is allowed to pick one of its neighbors, and to send it a message. The telephone k-multicast problem requires to compute a schedule with minimal number of...

This paper deals with the problem of broadcasting in minimum time in the telephone and message-passing models. Approximation algorithms are developed for arbitrary graphs, as well as for several restricted graph classes. In particular, an O( p n)-additive approximation algorithm is given for broadcasting in general graphs, and an O(log log n= log n...

A k- spanner of a connected graph G=(V, E) is a subgraph G consisting of all the vertices of V and a subset of the edges, with the additional property that the distance between any two vertices in G is larger than that distance in G by no more than a factor of k. This note concerns the problem of finding the sparsest 2-spanner in a given graph, and...

In the buy-at-bulk $k$-Steiner tree (or rent-or-buy$k$-Steiner tree) problem we are given a graph $G(V,E)$ with a setof terminals $T\subseteq V$ including a particular vertex $s$ calledthe root, and an integer $k\leq |T|$. There are two cost functionson the edges of $G$, a buy cost $b:E\longrightarrow \RR^+$ and a rentcost $r:E\longrightarrow \RR^+...

We consider the non-uniform multicommodity buy-at-bulknetworkdesign problem. In this problem we are given a graph $G(V,E)$withtwo cost functions on the edges, a buy cost $b:E\longrightarrow \RR^+$and a rent cost$r:E\longrightarrow\RR^+$, and a set of source-sink pairs$s_i,t_i\in V$ ($1\leq i\leq \alpha$)with each pair $i$ having a positivedemand $\...

The data migration problem is to compute an efficient plan for moving data stored on devices in a network from one configuration to another. We consider this problem with the objective of minimizing the sum of completion times of all storage devices. It is modeled by a transfer graph, where vertices represent the storage devices, and the edges indi...

Buy-at-bulk network design problems arise in settings where the costs for purchasing or installing equipment exhibit economies of scale. The objective is to build a network of cheapest cost to support a given multi-commodity ow demand between node pairs. We present approxi- mation algorithms for buy-at-bulk network design problems with costs on bot...

In the group Steiner problem we are given an edge-weighted graph G=(V,E,w) and m subsets of vertices . Each subset gi is called a group and the vertices in ⋃igi are called terminals. It is required to find a minimum weight tree that contains at least one terminal from every group.We present a poly-logarithmic ratio approximation for this problem wh...

In this paper we study the capacitated vertex cover prob- lem, a generalization of the well-known vertex cover problem. Given a graph G = (V;E), the goal is to cover all the edges by picking a mini- mum cover using the vertices. When we pick a vertex, we can cover up to a pre-specied number of edges incident on this vertex (its capac- ity). The pro...

The Directed Multicut (DM) problem is: given a simple directed graph G = (V, E) with positive capacities ue on the edges, and a set K ⊆ V × V of ordered pairs of nodes of G, find a minimum capacity K-multicut; C ⊆ E is a K-multicut if in G − C there is no (s, t)-path for any (s, t) ⫅ K. In the uncapacitated case (UDM) the goal is to find a minimum...