In set system auctions, a single buyer needs to purchase services from multiple competing providers, and the set of providers has a combinatorial structure; a popular example is provided by shortest path auctions [1, 7]. In [3] it has been observed that if such an auction is conducted using first-price rules, then, counterintuitively, the buyer’s payment may go down if some of the sellers are p...

The goal of a hub-based distance labeling scheme for a network G = (V,E) is to assign a small subset S(u) ⊆ V to each node u ∈ V , in such a way that for any pair of nodes u, v, the intersection of hub sets S(u) ∩ S(v) contains a node on the shortest uv-path. The existence of small hub sets, and consequently efficient shortest path processing algorithms, for road networks is an empirical observ...

So far we have studied the set covering problem, but not looked at any real life applications. The shortest superstring problem takes as input, several strings of different lengths and finds the shortest string that contains all the input strings as substrings. This is helpful in the genome project since it will allow researchers to determine entire coding regions from a collection of fragmente...

A many-to-many k-disjoint path cover (k-DPC for short) of a graph G joining the pairwise disjoint vertex sets S and T , each of size k, is a collection of k vertex-disjoint paths between S and T , which altogether cover every vertex of G. This is classified as paired, if each vertex of S must be joined to a specific vertex of T , or unpaired, if there is no such constraint. In this paper, we de...

In multiagent systems, we often have a set of agents each of which have a preference ordering over a set of items and one would like to know these preference orderings for various tasks, for example, data analysis, preference aggregation, voting etc. However, we often have a large number of items which makes it impractical to ask the agents for their complete preference ordering. In such scenar...

In this paper we focus on problems which do not admit a constant-factor approximation in polynomial time and explore how quickly their approximability improves as the allowed running time is gradually increased from polynomial to (sub-)exponential. We tackle a number of problems: For Min Independent Dominating Set, Max Induced Path, Forest and Tree, for any r(n), a simple, known scheme gives an...