Log In Sign Up

Equitable Division of a Path

by   Neeldhara Misra, et al.

We study fair resource allocation under a connectedness constraint wherein a set of indivisible items are arranged on a path and only connected subsets of items may be allocated to the agents. An allocation is deemed fair if it satisfies equitability up to one good (EQ1), which requires that agents' utilities are approximately equal. We show that achieving EQ1 in conjunction with well-studied measures of economic efficiency (such as Pareto optimality, non-wastefulness, maximum egalitarian or utilitarian welfare) is computationally hard even for binary additive valuations. On the algorithmic side, we show that by relaxing the efficiency requirement, a connected EQ1 allocation can be computed in polynomial time for any given ordering of agents, even for general monotone valuations. Interestingly, the allocation computed by our algorithm has the highest egalitarian welfare among all allocations consistent with the given ordering. On the other hand, if efficiency is required, then tractability can still be achieved for binary additive valuations with interval structure. On our way, we strengthen some of the existing results in the literature for other fairness notions such as envy-freeness up to one good (EF1), and also provide novel results for negatively-valued items or chores.


page 1

page 2

page 3

page 4


Equitable Allocations of Indivisible Goods

In fair division, equitability dictates that each participant receives t...

Pareto-Optimal Allocation of Indivisible Goods with Connectivity Constraints

We study the problem of allocating indivisible items to agents with addi...

On Approximate Envy-Freeness for Indivisible Chores and Mixed Resources

We study the fair allocation of undesirable indivisible items, or chores...

Finding Fair and Efficient Allocations When Valuations Don't Add Up

In this paper, we present new results on the fair and efficient allocati...

Two Algorithms for Additive and Fair Division of Mixed Manna

We consider a fair division model in which agents have positive, zero an...

On Interim Envy-Free Allocation Lotteries

With very few exceptions, recent research in fair division has mostly fo...

Almost Envy-Freeness in Group Resource Allocation

We study the problem of fairly allocating indivisible goods between grou...