9848793
Stochastic Steiner Trees Without a Root
This paper considers the Steiner tree problem in the model of two-stage stochastic optimization with recourse. This model, the focus of much recent research [11, 16, 8, 18], tries to capture the fact that many infrastructure planning problems have to be solved in the presence of uncertainty, and that we have make decisions knowing merely market forecasts (and not the precise set of demands); by the time the actual demands arrive, the costs may be higher due to inflation. 
 
In the context of the Stochastic Steiner Tree problem on a graph G = (V,E), the model can be paraphrased thus: on Monday, we are given a probability distribution π on subsets of vertices, and can build some subset EM of edges. On Tuesday, a set of terminals D materializes (drawn from the same distribution π). We now have to buy edges ET so that the set EM ∪ ET forms a Steiner tree on D. The goal is to minimize the expected cost of the solution. 
 
We give the first constant-factor approximation algorithm for this problem. To the best of our knowledge, this is the first O(1)-approximation for the stochastic version of a non sub-additive problem. In fact, algorithms for the unrooted stochastic Steiner tree problem we consider are powerful enough to solve the Multicommodity Rent-or-Buy problem, itself a topic of recent interest [3, 7, 15].
11033759
Oblivious network design
Consider the following network design problem: given a network <i>G = (V, E)</i>, source-sink pairs {<i>s</i><inf><i>i</i></inf>, <i>t</i><inf><i>i</i></inf>} arrive and desire to send a unit of flow between themselves. The cost of the routing is this: if edge <i>e</i> carries a total of <i>f</i><inf><i>e</i></inf> flow (from all the terminal pairs), the cost is given by Σ <inf><i>e</i></inf><i>l</i>(<i>f</i><inf><i>e</i></inf>), where <i>l</i> is some concave cost function; the goal is to minimize the total cost incurred. However, we want the routing to be <i>oblivious</i>: when terminal pair {<i>s</i><inf><i>i</i></inf>, <i>t</i><inf><i>i</i></inf>} makes its routing decisions, it does not know the current flow on the edges of the network, nor the identity of the other pairs in the system. Moreover, it does not even know the identity of the function <i>l</i>, merely knowing that <i>l</i> is a concave function of the total flow on the edge. How should it (obliviously) route its one unit of flow? Can we get competitive algorithms for this problem?In this paper, we develop a framework to model <i>oblivious network design</i> problems (of which the above problem is a special case), and give algorithms with poly-logarithmic competitive ratio for problems in this framework (and hence for this problem). Abstractly, given a problem like the one above, the solution is a multicommodity flow producing a "load" on each edge of <i>L</i><inf><i>e</i></inf> = <i>l</i>(<i>f</i><inf>1</inf>(<i>e</i>),<i>f</i><inf>2</inf>(<i>e</i>), ..., <i>f</i><inf><i>k</i></inf>(<i>e</i>)), and the total cost is given by an "aggregation function" agg (<i>L</i><inf><i>e</i>1</inf>,...,<i>L</i><inf><i>em</i></inf>) of the loads of all edges. Our goal is to develop oblivious algorithms that approximately minimize the total cost of the routing, knowing the aggregation function agg, but merely knowing that <i>l</i> lies in some class C, and having no other information about the current state of the network. Hence we want algorithms that are simultaneously "function-oblivious" as well as "traffic-oblivious".The aggregation functions we consider are the max and σ objective functions, which correspond to the well-known measures of <i>congestion</i> and <i>total cost</i> of a network; in this paper, we prove the following:• If the aggregation function is Σ, we give an oblivious algorithm with <i>O</i>(log<sup>2</sup> <i>n</i>) competitive ratio whenever the load function <i>l</i> is in the class of <i>monotone sub-additive functions</i>. (Recall that our algorithm is also "function-oblivious"; it works whenever each edge has a load function <i>l</i> in the class.)• For the case when the aggregation function is max, we give an oblivious algorithm with <i>O</i>(log<sup>2</sup> <i>n</i> log log <i>n</i>) competitive ratio, when the load function <i>l</i> is a <i>norm;</i> we also show that such a competitive ratio is not possible for general sub-additive functions.These are the first such general results about oblivious algorithms for network design problems, and we hope the ideas and techniques will lead to more and improved results in this area.
411060
Approximating unique games
The UNIQUE GAMES problem is the following: we are given a graph <i>G</i> = (<i>V, E</i>), with each edge <i>e</i> = (<i>u, v</i>) having a weight <i>w</i><inf><i>e</i></inf> and a permutation π<inf><i>uv</i></inf> on [<i>k</i>]. The objective is to find a labeling of each vertex <i>u</i> with a label <i>f</i><inf><i>u</i></inf> ∈ [<i>k</i>] to minimize the weight of unsatisfied edges---where an edge (<i>u, v</i>) is <i>satisfied</i> if <i>f</i><inf><i>v</i></inf> = π<inf><i>uv</i></inf>(<i>f</i><inf><i>u</i></inf>).The <i>Unique Games Conjecture</i> of Khot [8] essentially says that for each ε > 0, there is a <i>k</i> such that it is NP-hard to distinguish instances of Unique games with (1-ε) satisfiable edges from those with only ε satisfiable edges. Several hardness results have recently been proved based on this assumption, including optimal ones for Max-Cut, Vertex-Cover and other problems, making it an important challenge to prove or refute the conjecture.In this paper, we give an <i>O</i>(log <i>n</i>)-approximation algorithm for the problem of minimizing the number of unsatisfied edges in any Unique game. Previous results of Khot [8] and Trevisan [12] imply that if the optimal solution has OPT = ε<i>m</i> unsatisfied edges, semidefinite relaxations of the problem could give labelings with min {<i>k</i><sup>2</sup>ε<sup>1/5</sup>, (ε log <i>n</i>)<sup>1/2</sup>}<i>m</i> unsatisfied edges. In this paper we show how to round a LP relaxation to get an <i>O</i>(log <i>n</i>)-approximation to the problem; i.e., to find a labeling with only <i>O</i>(ε<i>m</i> log <i>n</i>) = <i>O</i>(OPT log <i>n</i>) unsatisfied edges.
37922436
Improved Bandwidth Approximation for Trees and Chordal Graphs
A linear arrangement of an n-vertex graph G=(V,E) is a one?one mapping f of the vertex set V onto the set n]={0,1,?,n?1}. The bandwidth of this linear arrangement is the maximum difference between the images of the endpoints of any edge in E(G). When the input graph G is a tree, the best known approximation algorithms for the minimum bandwidth linear arrangement (which are based on the principle of volume respecting embeddings) output a linear arrangement which has bandwidth within O(log3n) of the optimal bandwidth. In this paper, we present a simple randomized O(log2.5n)-approximation algorithm for bandwidth minimization on trees. We also show that a close variant of this algorithm gives a similar performance guarantee for chordal graphs.
47205636
Approximation Algorithms for the Unsplittable Flow Problem
We present approximation algorithms for the unsplittable flow problem (UFP) on undirected graphs. As is standard in this line of research, we assume that the maximum demand is at most the minimum capacity. We focus on the non-uniform capacity case in which the edge capacities can vary arbitrarily over the graph. Our results are: - For undirected graphs we obtain a O(??-1 log2 n) approximation ratio, where n is the number of vertices, ? the maximum degree, and ? the expansion of the graph. Our ratio is capacity independent and improves upon the earlier O(??-1(cmax/cmin) log n) bound [15] for large values of cmax/cmin. Furthermore, if we specialize to the case where all edges have the same capacity, our algorithm gives an O(??-1 log n) approximation, which matches the performance of the best-known algorithm [15] for this special case. - For certain strong constant-degree expanders considered by Frieze [10] we obtain an O(? log n) approximation for the uniform capacity case, improving upon the current O(log n) approximation. - For UFP on the line and the ring, we give the first constant-factor approximation algorithms. Previous results addressed only the uniform capacity case. - All of the above results improve if the maximum demand is bounded away from the minimum capacity.Our results are based on randomized rounding followed by greedy alteration and are inspired by the use of this idea in recent work [21, 9].
100323
Tree based MPLS routing
MPLS (MultiProtocol Label Switching) is a new technology proposed by the IETF [4,10] for network routing, and is being increasingly deployed by the largest Internet service providers. The MPLS technology differs from conventional network protocols in a crucial way: instead of reading the entire packet header at all switching points, the analysis of the packet header is done just once, when the packet header is assigned a stack of labels, and thenceforth, each switching point or router just gets to look at the label at the top of the stack (and the ingress edge), and based only on this information, it has to make a decision about the next-hop node [17,16]. In another departure from conventional routing and in particular from IP source routing, where the entire packet route is explicitly put in the header and popped off along the route, the router can not only pop the top label, it can push other labels on top of the stack.The two parameters of interest in designing MPLS routing protocols are the number of labels used, and the depth of the stack used for routing. Clearly, both cannot be simultaneously minimized, and there is often an interesting trade-off between label size and stack depth: it is obvious that if k labels are used, one must have a stack depth of logk n.In fact, it was not known whether this bound could be achieved even for trees; the best stack depth previously achieved with a constant number of labels was O(log2 n). In this paper, we show that one can indeed get asymptotically optimal upper bounds and route on trees using k labels and a maximum stack depth of O(logk n), and that this trade-off can be achieved using a simpler and more intuitive protocol than the one given in [9]. These tree-routing ideas are then shown to give better routing protocols for planar graphs as well. In particular, we show how to route along near-shortest paths (of length at most (1 + ε) times the shortest-path) with O(log2 n/ε) labels and logarithmic stack depth. We also apply them to graphs with smaller separators, including most large ISP networks.
1782369
Designing and executing scientific workflows with a programmable integrator
MOTIVATION
As in many other fields of science, computational methods in molecular biology need to intersperse information access and algorithm execution in a computational workflow. Users often find difficulties when transferring data between data sources and applications. In most cases there is no standard solution for workflow design and execution and tailored scripting mechanisms are implemented in a case by case basis.


RESULTS
In this paper, we present a general purpose 'programmable integrator' that can access information from a variety of sources in a coordinated manner. Its usefulness in complex bioinformatics applications is claimed and supported by some application examples.


AVAILABILITY
Tools are freely available to non-profit educations and research institutions. Usage by commercial organizations requires a license agreement. Software requirements: Java v1.3 (http://java.sun.com), Xerces XML Parser (http://xml.apache.org/xerces-j) and Kweelt implementation of XQuery (http://kweelt.sourceforge.net/).
575078
An Approach for Detecting Self-propagating Email Using Anomaly Detection
This paper develops a new approach for detecting self-propagating email viruses based on statistical anomaly detection. Our approach assumes that a key objective of an email virus attack is to eventually overwhelm mail servers and clients with a large volume of email traffic. Based on this assumption, the approach is designed to detect increases in traffic volume over what was observed during the training period. This paper describes our approach and the results of our simulation-based experiments in assessing the effectiveness of the approach in an intranet setting. Within the simulation setting, our results establish that the approach is effective in detecting attacks all of the time, with very few false alarms. In addition, attacks could be detected sufficiently early so that clean up efforts need to target only a fraction of the email clients in an intranet.
26737462
The Parallel Complexity of Tree Embedding Problems
Abstract The question of the sequential complexity of various tree embedding problems arises in the recent work of Robertson and Seymour on graph miners; here we consider the parallel complexity of such problems. In particular, we present two CREW PRAM algorithms: an O (log 3 n ) time randomized algorithm for determining whether there is a topological embedding of one rooted tree in another and an O (log 2 n log log n ) time deterministic algorithm for determining whether or not a rooted tree with a degree constraint is a minor of a general rooted tree. These algorithms are two examples of a general technique that can be used for solving other problems on trees.
878886
Verification of embedded memory systems using efficient memory modeling
We describe verification techniques for embedded memory systems using efficient memory modeling (EMM), without explicitly modeling each memory bit. We extend our previously proposed approach of EMM in bounded model checking (BMC) for a single read/write port single memory system, to more commonly occurring systems with multiple memories, having multiple read and write ports. More importantly, we augment such EMM to providing correctness proofs, in addition to finding real bugs as before. The novelties of our verification approach are in (a) combining EMM with a proof-based abstraction that preserves the correctness of a property up to a certain analysis depth of SAT-based BMC, and (b) modeling arbitrary initial memory state precisely and thereby providing inductive proofs using SAT-based BMC for embedded memory systems. Similar to the previous approach, we construct a verification model by eliminating memory arrays, but retaining the memory interface signals with their control logic and adding constraints on those signals at every analysis depth to preserve the data forwarding semantics. The size of these EMM constraints depends quadratically on the number of memory accesses and the number of read and write ports; and linearly on the address and data widths and the number of memories. We show the effectiveness of our approach on several industry designs and software programs.
19362396
Finding Largest Common Embeddable Subtrees
We consider the problem of determining the largest tree embeddable in two labeled trees T and T′, where the embedding relation is one of subgraph isomorphism or topological embedding. This problem is a generalization of classical tree pattern matching where the problem is to determine if one labeled tree is isomorphic to a subgraph of another. In this paper, we present a general framework for the variations on the problem, for the two embedding relations and for different assumptions about labeling of nodes in the trees. Our general paradigm provides sequential and parallel algorithms for the various subproblems, many of which have no other known solutions.