427 research outputs found
Algorithms for Secretary Problems on Graphs and Hypergraphs
We examine several online matching problems, with applications to Internet
advertising reservation systems. Consider an edge-weighted bipartite graph G,
with partite sets L, R. We develop an 8-competitive algorithm for the following
secretary problem: Initially given R, and the size of L, the algorithm receives
the vertices of L sequentially, in a random order. When a vertex l \in L is
seen, all edges incident to l are revealed, together with their weights. The
algorithm must immediately either match l to an available vertex of R, or
decide that l will remain unmatched.
Dimitrov and Plaxton show a 16-competitive algorithm for the transversal
matroid secretary problem, which is the special case with weights on vertices,
not edges. (Equivalently, one may assume that for each l \in L, the weights on
all edges incident to l are identical.) We use a similar algorithm, but
simplify and improve the analysis to obtain a better competitive ratio for the
more general problem. Perhaps of more interest is the fact that our analysis is
easily extended to obtain competitive algorithms for similar problems, such as
to find disjoint sets of edges in hypergraphs where edges arrive online. We
also introduce secretary problems with adversarially chosen groups. Finally, we
give a 2e-competitive algorithm for the secretary problem on graphic matroids,
where, with edges appearing online, the goal is to find a maximum-weight
acyclic subgraph of a given graph.Comment: 15 pages, 2 figure
The Post-Agreement Negotiation Process: The Problems of Ratifying International Environmental Agreements
National ratification of international environmental agreements is a prime example of post-agreement negotiations. It is often the first subprocess in a larger process of sustained negotiations that occur after international accords are concluded, focused on implementation of those accords. Certainly, implementation of negotiated agreements involves legal, political, verification, and enforcement activities at both domestic and international levels. Many of these activities, including ratification, are characterized by negotiations between various stakeholders to reach mutually beneficial and acceptable means to achieve national implementation of, and compliance with, treaty provisions.
This paper places ratification negotiations within the larger conceptual context of post-agreement negotiations, with the goal of understanding and explaining problems of treaty compliance. An empirical analysis is conducted to assess the impact of various inherent and situational factors on problems in the ratification process. Ultimately, we are interested in identifying ways of improving the international negotiation process that initiated these later problems in implementation
Single-Sink Network Design with Vertex Connectivity Requirements
We study single-sink network design problems in undirected graphs
with vertex connectivity requirements. The input to these problems
is an edge-weighted undirected graph , a sink/root vertex
, a set of terminals , and integer . The goal is
to connect each terminal to via emph{vertex-disjoint}
paths. In the {em connectivity} problem, the objective is to find a
min-cost subgraph of that contains the desired paths. There is a
-approximation for this problem when cite{FleischerJW}
but for , the first non-trivial approximation was obtained
in the recent work of Chakraborty, Chuzhoy and Khanna
cite{ChakCK08}; they describe and analyze an algorithm with an
approximation ratio of where .
In this paper, inspired by the results and ideas in cite{ChakCK08},
we show an -approximation bound for a simple
greedy algorithm. Our analysis is based on the dual of a natural
linear program and is of independent technical interest. We use the
insights from this analysis to obtain an -approximation for the more general single-sink {em
rent-or-buy} network design problem with vertex connectivity
requirements. We further extend the ideas to obtain a
poly-logarithmic approximation for the single-sink {em buy-at-bulk}
problem when and the number of cable-types is a fixed
constant; we believe that this should extend to any fixed . We
also show that for the non-uniform buy-at-bulk problem, for each
fixed , a small variant of a simple algorithm suggested by
Charikar and Kargiazova cite{CharikarK05} for the case of
gives an approximation for larger .
These results show that for each of these problems, simple and
natural algorithms that have been developed for have good
performance for small
Pruning 2-Connected Graphs
Given an edge-weighted undirected graph with a specified set of
terminals, let the emph{density} of any subgraph be the ratio of
its weight/cost to the number of terminals it contains. If is
2-connected, does it contain smaller 2-connected subgraphs of
density comparable to that of ? We answer this question in the
affirmative by giving an algorithm to emph{prune} and find such
subgraphs of any desired size, at the cost of only a logarithmic
increase in density (plus a small additive factor).
We apply the pruning techniques to give algorithms for two NP-Hard
problems on finding large 2-vertex-connected subgraphs of low cost;
no previous approximation algorithm was known for either problem. In
the kv problem, we are given an undirected graph with edge
costs and an integer ; the goal is to find a minimum-cost
2-vertex-connected subgraph of containing at least
vertices. In the bv problem, we are given the graph with edge
costs, and a budget ; the goal is to find a 2-vertex-connected
subgraph of with total edge cost at most that maximizes
the number of vertices in . We describe an
approximation for the kv problem, and a bicriteria approximation
for the bv problem that gives an
approximation, while violating the budget by a factor of at most
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