Coalition formation is a key topic in multiagent systems. One may prefer a coalition structure that maximizes the sum of the values of the coalitions, but often the number of coalition structures is too large to allow exhaustive search for the optimal one. Furthermore, finding the optimal coalition structure is NP-complete. But then, can the coalition structure found via a partial search be guaranteed to be within a bound from optimum? We show that none of the previous coalition structure generation algorithms can establish any bound because they search fewer nodes than a threshold that we show necessary for establishing a bound. We present an algorithm that establishes a tight bound within this minimal amount of search, and show that any other algorithm would have to search strictly more. The fraction of nodes needed to be searched approaches zero as the number of agents grows. If additional time remains, our anytime algorithm searches further, and establishes a progressively lower tight bound. Surprisingly, just searching one more node drops the bound in half. As desired, our algorithm lowers the bound rapidly early on, and exhibits diminishing returns to computation. It also significantly outperforms its obvious contenders. Finally, we show how to distribute the desired

Unit disk graphs are intersection graphs of circles of unit radius in the plane. We present simple and provably good heuristics for a number of classical NP-hard optimization problems on unit disk graphs. The problems considered include maximum independent set, minimum vertex cover, minimum coloring and minimum dominating set. We also present an on-line coloring heuristic which achieves a competitive ratio of 6 for unit disk graphs. Our heuristics do not need a geometric representation of unit disk graphs. Geometric representations are used only in establishing the performance guarantees of the heuristics. Several of our approximation algorithms can be extended to intersection graphs of circles of arbitrary radii in the plane, intersection graphs of regular polygons, and to intersection graphs of higher dimensional regular objects.

This paper presents eMediator, an electronic commerce server prototype that demonstrates ways in which algorithmic support and game-theoretic incentive engineering can jointly improve the efficiency of ecommerce. eAuctionHouse, the configurable auction server, includes a variety of generalized combinatorial auctions and exchanges, pricing schemes, bidding languages, mobile agents, and user support for choosing an auction type. We introduce two new logical bidding languages for combinatorial markets: the XOR bidding language and the OR-of-XORs bidding language. Unlike the traditional OR bidding language, these are fully expressive. They therefore enable the use of the Clarke-Groves pricing mechanism for motivating the bidders to bid truthfully. eAuctionHouse also supports supply/demand curve bidding. eCommitter, the leveled commitment contract optimizer, determines the optimal contract price and decommitting penalties for a variety of leveled commitment contracting mechanisms, taking into account that rational agents will decommit strategically in Nash equilibrium. It also determines the optimal decommitting strategies for any given leveled commitment contract. eExchangeHouse, the safe exchange planner, enables unenforced anonymous exchanges by dividing the exchange into chunks and sequencing those chunks to be delivered safely in alternation between the buyer and the seller.

We attempt to reconcile the two distinct views of approximation classes: syntactic and computational. Syntactic classes such as MAX SNP permit structural results and have natural complete problems, while computational classes such as APX allow us to work with classes of problems whose approximability is well-understood. Our results provide a syntactic characterization of computational classes, and give a computational framework for syntactic classes. We compare the syntactically defined class MAX SNP with the computationally defined class APX, and show that every problem in APX can be “placed ” (i.e. has approximation preserving reduction to a problem) in MAX SNP. Our methods introduce a general technique for creating approximation-preserving reductions which show that any “well ” approximable problem can be reduced in an approximation-preserving manner to a problem which is hard to approximate to corresponding factors. We demonstrate this technique by applying it to the classes RMAX(2) and MIN F+Π2(1)which have the clique problem and the set cover problem, respectively, as complete problems. We use the syntactic nature of MAX SNP to define a general paradigm, non-oblivious local search, useful for developing simple yet efficient approximation algorithms. We show that such algorithms can find good approximations for all MAX SNP problems, yielding approximation ratios comparable to the best-known for a variety of specific MAX SNP-hard problems. Non-oblivious local search provably out-performs standard local search in both the degree of approximation achieved and the efficiency of the resulting algorithms.

We obtain improved algorithms for finding small vertex covers in bounded degree graphs and hypergraphs. We use semidefinite programming to relax the problems, and introduce new rounding techniques for these relaxations. On graphs with maximum degree at most Δ, the algorithm achieves a performance ratio of 2 - (1 - o(1)) 2 ln ln \Delta ln \Delta for large \Delta, which improves the previously known ratio of 2 \Gamma log \Delta+O(1) \Delta obtained by Halldórsson and Radhakrishnan. Using similar techniques, we also present improved approximations for the vertex cover problem in hypergraphs. For k-uniform hypergraphs with n vertices, we achieve a ratio of k \Gamma (1 \Gamma o(1)) k ln ln n ln n for large n, and for k-uniform hypergraphs with maximum degree at most \Delta, the algorithm achieves a ratio of k \Gamma (1 \Gamma o(1)) k(k\Gamma1) ln ln \Delta ln \Delta for large \Delta. These results considerably improve the previous best ratio of k(1\Gammac=\Delta 1 k\Gamma1 ) for bounded degree k-uniform hypergraphs, and k(1 \Gamma c=n k\Gamma1 k ) for general k-uniform hypergraphs, both obtained by Krivelevich. Using similar techniques, we also obtain an approximation algorithm for the weighted independent set problem, matching a recent result of Halldórsson.

This paper presents two algorithms based on the horizontal and vertical pattern discovery paradigms that find the connected subgraphs that have a sufficient number of edge-disjoint embeddings in a single large undirected labeled sparse graph. These algorithms use three different methods to determine the number of the edge-disjoint embeddings of a subgraph that are based on approximate and exact maximum independent set computations and use it to prune infrequent subgraphs. Experimental evaluation on real datasets from various domains show that both algorithms achieve good performance, scale well to sparse input graphs with more than 100,000 vertices, and significantly outperform a previously developed algorithm.

... for short, is one of the ~implest, most efficient, and most thoroughly studied methods for finding independent sets in graphs. We show that it surprisingly achieves a performance ratio of (A+ 2)/3 for approximating inde-pendent sets in graphs with degree bounded by A. The analysis directs us towards a simple parallel and dis-tributed algorithm with identical performance, which on constant-degree graphs runs in O(log ” n) time us-ing linear number of processors. We also analyze the Greedy algorithm when run in combination with a frac-tional relaxation technique of Nemhauser and Trotter, and obtain an improved (2Z + 3)/5 performance ratio on graphs with average degree ~. Finally, we introduce a generally applicable technique for improving the approximation ratios of independent set algorithms, and illustrate it by improving the per-formance ratio of Greedy for large ∆.

The focus of this study is to clarify the approximability of weighted versions of the maximum independent set problem. In particular, we report improved performance ratios in bounded-degree graphs, inductive graphs, and general graphs, as well as for the unweighted problem in sparse graphs. Where possible, the techniques are applied to related hereditary subgraph and subset problem, obtaining ratios better than previously reported for e.g. Weighted Set Packing, Longest Common Subsequence, and Independent Set in hypergraphs.

Abstract. Kernelization is a strong and widely-applied technique in parameterized complexity. In a nutshell, a kernelization algorithm, or simply a kernel, is a polynomial-time transformation that transforms any given parameterized instance to an equivalent instance of the same problem, with size and parameter bounded by a function of the parameter in the input. A kernel is polynomial if the size and parameter of the output are polynomially-bounded by the parameter of the input. In this paper we develop a framework which allows showing that a wide range of FPT problems do not have polynomial kernels. Our evidence relies on hypothesis made in the classical world (i.e. nonparametric complexity), and evolves around a new type of algorithm for classical decision problems, called a distillation algorithm, which might be of independent interest. Using the notion of distillation algorithms, we develop a generic lower-bound engine which allows us to show that a variety of FPT problems, fulfilling certain criteria, cannot have polynomial kernels unless the polynomial hierarchy collapses. These problems include k-Path, k-Cycle, k-Exact Cycle, k-Short Cheap Tour, k-Graph Minor Order Test, k-Cutwidth, k-Search Number, k-Pathwidth, k-Treewidth, k-Branchwidth, and several optimization problems parameterized by treewidth or cliquewidth. 1

We present here 2-approximation algorithms for several node deletion and edge deletion biclique problems and for an edge deletion clique problem. The biclique problem is to find a node induced subgraph which is bipartite and complete. The objective is to minimize the total weight of nodes or edges deleted so that the remaining subgraph is bipartite complete. Several variants of the biclique problem are studied here where the problem is defined on bipartite graph or on general graphs with or without the requirement that each side of the bipartition forms an independent set. The maximum clique problem is formulated as maximizing the number (or weight) of edges in the complete subgraph. A 2-approximation algorithm is given for the minimum edge deletion version of this problem. The approximation algorithms given here are derived as a special case of an approximation technique devised for a class of formulations introduced by Hochbaum [Hoc96]. All approximation algorithms described (and the...