C. Pandu Rangan

Publications

1 Computing Maximum Uniquely Restricted Matchings in Restricted Interval Graphs

Authors: Swapnil Gupta, C. Pandu Rangan

Abstract:

A uniquely restricted matching is defined to be a matching M whose matched vertices induces a sub-graph which has only one perfect matching. In this paper, we make progress on the open question of the status of this problem on interval graphs (graphs obtained as the intersection graph of intervals on a line). We give an algorithm to compute maximum cardinality uniquely restricted matchings on certain sub-classes of interval graphs. We consider two sub-classes of interval graphs, the former contained in the latter, and give O(|E|^2) time algorithms for both of them. It is to be noted that both sub-classes are incomparable to proper interval graphs (graphs obtained as the intersection graph of intervals in which no interval completely contains another interval), on which the problem can be solved in polynomial time.

Keywords: Matching, uniquely restricted matching, interval graph, induced matching, design and analysis of algorithms, witness counting

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Abstracts

2 The Hospitals Residents Problem with Bounded Length Preference List under Social Stability

Authors: Ashish Shrivastava, C. Pandu Rangan

Abstract:

In this paper, we consider The Hospitals Residents problem with Social Stability (HRSS), where hospitals and residents can communicate only through the underlying social network. Those residents and hospitals which don not have any social connection between them can not communicate and hence they cannot be a social blocking pair with respect to a socially stable matching in an instance of hospitals residents problem with social stability. In large scale matching like NRMP or Scottish medical matching scheme etc. where set of agents, as well as length of preference lists, are very large, social stability is a useful notion in which members of a blocking pair could block a matching if and only if they know the existence of each other. Thus the notion of social stability in hospitals residents problem allows us to increase the cardinality of the matching without taking care of those blocking pairs which are not socially connected to each other. We know that finding a maximum cardinality socially stable matching, in an instance, of HRSS is NP-hard. This motivates us to solve this problem with bounded length preference lists on one side. In this paper, we have presented a polynomial time algorithm to compute maximum cardinality socially stable matching in a HRSS instance where residents can give at most two length and hospitals can give unbounded length preference list. Preference lists of residents and hospitals will be strict in nature.

Keywords: matching under preference, socially stable matching, the hospital residents problem, the stable marriage problem

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1 Computing Maximum Uniquely Restricted Matchings in Restricted Interval Graphs

Authors: Swapnil Gupta, C. Pandu Rangan

Abstract:

A uniquely restricted matching is defined to be a matching M whose matched vertices induces a sub-graph which has only one perfect matching. In this paper, we make progress on the open question of the status of this problem on interval graphs (graphs obtained as the intersection graph of intervals on a line). We give an algorithm to compute maximum cardinality uniquely restricted matchings on certain sub-classes of interval graphs. We consider two sub-classes of interval graphs, the former contained in the latter, and give O(|E|^2) time algorithms for both of them. It is to be noted that both sub-classes are incomparable to proper interval graphs (graphs obtained as the intersection graph of intervals in which no interval completely contains another interval), on which the problem can be solved in polynomial time.

Keywords: Matching, uniquely restricted matching, interval graph, induced matching, witness counting

Procedia PDF Downloads 207