
Erel Segal-HaleviBar Ilan University | BIU · Department of Computer Science
Erel Segal-Halevi
M.Sc. computer science
About
113
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Introduction
I am interested in collaboration in any topic related to fair division, cake-cutting and economies with land.
My Ph.D. research is about fair division of land. It combines algorithms, geometry and economics.
Additional affiliations
January 2011 - December 2013
Publications
Publications (113)
We consider the problem of fair division of a two dimensional heterogeneous good among several agents. Applications include division of land as well as ad space in print and electronic media. Classical cake cutting protocols either consider a one-dimensional resource, or allocate each agent several disconnected pieces. In practice, however, the two...
To date, a variety of automated negotiation agents have been created. While each of these agents has been shown to be effective in negotiating with people in specific environments, they typically lack the natural language processing support required to enable real-world types of interactions. To address this limitation, we present NegoChat-A, an ag...
We consider the classic problem of envy-free division of a heterogeneous good (aka the cake) among multiple agents. It is well known that if each agent must receive a contiguous piece then there is no finite protocol for the problem, whenever there are 3 or more agents. This impossibility result, however, assumes that the entire cake must be alloca...
This paper presents PLIS, an open source Probabilistic Lexical Inference System which combines two functionalities: (i) a tool for integrating lexical inference knowledge from diverse resources, and (ii) a framework for scoring textual inferences based on the integrated knowledge. We provide PLIS with two probabilistic implementation of this framew...
We study fair division of indivisible chores among $n$ agents with additive cost functions using the popular fairness notion of maximin share (MMS). Since MMS allocations do not always exist for more than two agents, the goal has been to improve its approximations and identify interesting special cases where MMS allocations exists. We show the exis...
Two prominent objectives in social choice are utilitarian - maximizing the sum of agents' utilities, and leximin - maximizing the smallest agent's utility, then the second-smallest, etc. Utilitarianism is typically computationally easier to attain but is generally viewed as less fair. This paper presents a general reduction scheme that, given a uti...
We revisit the setting of fairly allocating indivisible items when agents have different weights representing their entitlements. First, we propose a parameterized family of relaxations for weighted envy-freeness and the same for weighted proportionality; the parameters indicate whether smaller-weight or larger-weight agents are given a higher prio...
Leximin is a common approach to multi-objective optimization, frequently employed in fair division applications. In leximin optimization, one first aims to maximize the smallest objective value; subject to this, one maximizes the second-smallest objective; and so on. Often, even the single-objective problem of maximizing the smallest value cannot b...
We consider the allocation of indivisible objects among agents with different valuations, which can be positive or negative. An egalitarian allocation is an allocation that maximizes the smallest value given to an agent; finding such an allocation is NP-hard. We present a simple polynomial-time algorithm that finds an allocation that is Pareto-effi...
In fair division of indivisible goods, l-out-of-d maximin share (MMS) is the value that an agent can guarantee by partitioning the goods into d bundles and choosing the l least preferred bundles. Most existing works aim to guarantee to all agents a constant fraction of their 1-out-of-n MMS. But this guarantee is sensitive to small perturbation in a...
Charity is typically done either by individual donors, who donate money to the charities that they support, or by centralized organizations such as governments or municipalities, which collect the individual contributions and distribute them among a set of charities. On the one hand, individual charity respects the will of the donors but may be ine...
Leximin is a common approach to multi-objective optimization, frequently employed in fair division applications. In leximin optimization, one first aims to maximize the smallest objective value; subject to this, one maximizes the second-smallest objective; and so on. Often, even the single-objective problem of maximizing the smallest value cannot b...
We study fair allocation of indivisible goods among additive agents with feasibility constraints. In these settings, every agent is restricted to get a bundle among a specified set of feasible bundles. Such scenarios have been of great interest to the AI community due to their applicability to real-world problems. Following some impossibility resul...
Maximum bipartite matching is a fundamental algorithmic problem which can be solved in polynomial time. We consider a natural variant in which there is a separation constraint: the vertices on one side lie on a path or a grid, and two vertices that are close to each other are not allowed to be matched simultaneously. We show that the problem is har...
We consider allocating indivisible chores among agents with different cost functions, such that all agents receive a cost of at most a constant factor times their maximin share. The state-of-the-art was presented in In EC 2021 by Huang and Lu. They presented a non-polynomial-time algorithm, called HFFD, that attains an 11/9 approximation, and a pol...
Cake cutting is a classic fair division problem, with the cake serving as a metaphor for a heterogeneous divisible resource. Recently, it was shown that for any number of players with arbitrary preferences over a cake, it is possible to partition the players into groups of any desired size and divide the cake among the groups so that each group rec...
Cake cutting is a classic fair division problem, with the cake serving as a metaphor for a heterogeneous divisible resource. Recently, it was shown that for any number of players with arbitrary preferences over a cake, it is possible to partition the players into groups of any desired size and divide the cake among the groups so that each group rec...
A d-partite hypergraph is called fractionally balanced if there exists a non-negative, not identically zero, function on its edge set that has constant degrees in each vertex side. Using a topological version of Hall’s theorem we prove lower bounds on the matching number of such hypergraphs. These bounds yield rainbow versions of the KKM theorem fo...
We analyze the run-time complexity of computing allocations that are both fair and maximize the utilitarian social welfare, defined as the sum of agents’ utilities. We focus on two tractable fairness concepts: envy-freeness up to one item (EF1) and proportionality up to one item (PROP1). We consider two computational problems: (1) Among the utilita...
We study the problem of fairly allocating a divisible resource, also known as cake cutting, with an additional requirement that the shares that different agents receive should be sufficiently separated from one another. This captures, for example, constraints arising from social distancing guidelines. While it is sometimes impossible to allocate a...
In a classical “jury theorem” setting, the collective performance of a group of independent decision-makers is maximized by a voting rule that assigns weight to individuals compatibly with skills. The primary concern is that such weighted voting interferes with majoritarianism, since excessive power may be granted to a competent minority. In this p...
We revisit the setting of fairly allocating indivisible items when agents have different weights representing their entitlements. First, we propose a parameterized family of relaxations for weighted envy-freeness and the same for weighted proportionality; the parameters indicate whether smaller-weight or larger-weight agents should be given a highe...
In the classical cake-cutting problem, strategy-proofness is a very costly requirement in terms of fairness: for n=2\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$n=2$...
When assets are to be divided among several partners, for example, a partnership split, fair division theory can be used to determine a fair allocation. The applicability of existing approaches is limited as they either treat assets as divisible resources that end up being shared among participants or deal with indivisible objects providing only ap...
In many developing countries, the total electricity demand is larger than the limited generation capacity of power stations. Many countries adopt the common practice of routine load shedding - disconnecting entire regions from the power supply - to maintain a balance between demand and supply. Load shedding results in inflicting hardship and discom...
In fair division of indivisible goods, ℓ-out-of-d maximin share (MMS) is the value that an agent can guarantee by partitioning the goods into d bundles and choosing the ℓ least preferred bundles. Most existing works aim to guarantee to all agents a constant fraction of their 1-out-of-n MMS. But this guarantee is sensitive to small perturbation in a...
We consider the problem of fairly and efficiently matching agents to indivisible items, under capacity constraints. In this setting, we are given a set of categorized items. Each category has a capacity constraint (the same for all agents), that is an upper bound on the number of items an agent can get from each category. Our main result is a polyn...
We consider a variant of the $n$-way number partitioning problem, in which some fixed number $s$ of items can be split between two or more bins. We show a two-way polynomial-time reduction between this variant and a second variant, in which the maximum bin sum must be within a pre-specified interval. We prove that the second variant can be solved i...
Rental harmony is the problem of assigning rooms in a rented house to tenants with different preferences, and simultaneously splitting the rent among them, such that no tenant envies the bundle (room and price) given to another tenant. Various researchers have studied this problem mainly under two incompatible assumptions: the miserly tenants assum...
The paper considers fair allocation of resources that are already allocated in an unfair way. This setting requires a careful balance between the fairness considerations and the rights of the present owners. The paper presents re-division algorithms that attain various trade-off points between fairness and ownership rights, in various settings diff...
Using two lab experiments, we investigate the real-life performance of envy-free and proportional cake-cutting procedures with respect to fairness and preference manipulation. Although the observed subjects' strategic behavior eliminates the fairness guarantees of envy-free procedures, we nonetheless find evidence that suggests that envy-free proce...
We study the problem of fairly allocating a set of m indivisible chores (items with non-positive value) to n agents. We consider the desirable fairness notion of 1-out-of-d maximin share (MMS) -- the minimum value that an agent can guarantee by partitioning items into d bundles and receiving the least valued bundle -- and focus on ordinal approxima...
We revisit the setting of fairly allocating indivisible items when agents have different weights representing their entitlements. First, we propose a parameterized family of relaxations for weighted envy-freeness and the same for weighted proportionality; the parameters indicate whether smaller-weight or larger-weight agents should be given a highe...
A matching in a bipartite graph with parts X and Y is called envy-free, if no unmatched vertex in X is a adjacent to a matched vertex in Y. Every perfect matching is envy-free, but envy-free matchings exist even when perfect matchings do not. We prove that every bipartite graph has a unique partition such that all envy-free matchings are contained...
An algorithm for number-partitioning is called value-monotone if whenever one of the input numbers increases, the objective function (the largest sum or the smallest sum of a subset in the output) weakly increases. This note proves that the List Scheduling algorithm and the Longest Processing Time algorithm are both value-monotone. This is in contr...
Fair division of land is an important practical problem that is commonly handled either by hiring assessors or by selling and dividing the proceeds. A third way to divide land fairly is via algorithms for fair cake-cutting. Such un-intermediated methods are not only cheaper than an assessor but also theoretically fairer since they guarantee each ag...
In fair division of indivisible goods, l-out-of-d maximin share (MMS) is the value that an agent can guarantee by partitioning the goods into d bundles and choosing the l least preferred bundles. Most existing works aim to guarantee to all agents a constant fraction of their one-out-of-n MMS. But this guarantee is sensitive to small perturbation in...
We study the recently introduced cake-cutting setting in which the cake is represented by an undirected graph. This generalizes the canonical interval cake and allows for modeling the division of road networks. We show that when the graph is a forest, an allocation satisfying the well-known criterion of maximin share fairness always exists. Our res...
This paper is part of an ongoing endeavor to bring the theory of fair division closer to practice by handling requirements from real-life applications. We focus on two requirements originating from the division of land estates: (1) each agent should receive a plot of a usable geometric shape, and (2) plots of different agents must be physically sep...
We present an ascending-price mechanism for a multi-sided market with a variety of participants, such as manufacturers, logistics agents, insurance providers, and assemblers. Each deal in the market may consist of a combination of agents from separate categories, and different such combinations are simultaneously allowed. This flexibility lets mult...
In two-sided markets, Myerson and Satterthwaite's impossibility theorem states that one can not maximize the gain-from-trade while also satisfying truthfulness, individual-rationality and no deficit. Attempts have been made to circumvent Myerson and Satterthwaite's result by attaining approximately-maximum gain-from-trade: the double-sided auctions...
We study the problem of fairly allocating a divisible resource, also known as cake cutting, with an additional requirement that the shares that different agents receive should be sufficiently separated from one another. This captures, for example, constraints arising from social distancing guidelines. While it is sometimes impossible to allocate a...
We study fair allocation of indivisible goods among additive agents with feasibility constraints. In these settings, every agent is restricted to get a bundle among a specified set of feasible bundles. Such scenarios have been of great interest to the AI community due to their applicability to real-world problems. Following some impossibility resul...
This paper is part of an ongoing endeavor to bring the theory of fair division closer to practice by handling requirements from real-life applications. We focus on two requirements originating from the division of land estates: (1) each agent should receive a plot of a usable geometric shape, and (2) plots of different agents must be physically sep...
We study the recently introduced cake-cutting setting in which the cake is represented by an undirected graph. This generalizes the canonical interval cake and allows for modeling the division of road networks. We show that when the graph is a forest, an allocation satisfying the well-known criterion of maximin share fairness always exists. Our res...
In the classic problem of fair cake-cutting, a single interval (“cake”) has to be divided among n agents with different value measures, giving each agent a single sub-interval with a value of at least 1∕n of the total. This paper studies a generalization in which the cake is made of m disjoint intervals, and each agent should get at most k sub-inte...
A fundamental result in cake cutting states that for any number of players with arbitrary preferences over a cake, there exists a division of the cake such that every player receives a single contiguous piece and no player is left envious. We generalize this result by showing that it is possible to partition the players into groups of any desired s...
We study the problem of fairly allocating a divisible resource, also known as cake cutting, with an additional requirement that the shares that different agents receive should be sufficiently separated from one another. This captures, for example, constraints arising from social distancing guidelines. While it is sometimes impossible to allocate a...
We study the computational complexity of computing allocations that are both fair and maximize the utilitarian social welfare, i.e., the sum of utilities reported by the agents. We focus on two tractable fairness concepts: envy-freeness up to one item (EF1) and proportionality up to one item (PROP1). In particular, we consider the following two com...
A d-partite hypergraph is called *fractionally balanced* if there exists a non-negative, not identically zero, function on its edge set that has constant degrees in each vertex side. Using a topological version of Hall's theorem we prove lower bounds on the matching number of such hypergraphs. These bounds yield rainbow versions of the KKM theorem...
Classic cake-cutting algorithms enable people with different preferences to divide among them a heterogeneous resource (“cake”) such that the resulting division is fair according to each agent’s individual preferences. However, these algorithms either ignore the geometry of the resource altogether or assume it is one-dimensional. In practice, it is...
In two-sided markets, Myerson and Satterthwaite's impossibility theorem states that one can not maximize the gain-from-trade while also satisfying truthfulness, individual-rationality and no deficit. Attempts have been made to circumvent Myerson and Satterthwaite's result by attaining approximately-maximum gain-from-trade: the double-sided auctions...
Competitive equilibrium (CE) is a fundamental concept in market economics. Its efficiency and fairness properties make it particularly appealing as a rule for fair allocation of resources among agents with possibly different entitlements. However, when the resources are indivisible, a CE might not exist even when there is one resource and two agent...
A fundamental result in cake cutting states that for any number of players with arbitrary preferences over a cake, there exists a division of the cake such that every player receives a single contiguous piece and no player is left envious. We generalize this result by showing that it is possible to partition the players into groups of any desired s...
Rental Harmony is the problem of assigning rooms in a rented house to tenants with different preferences, and simultaneously splitting the rent among them, such that no tenant envies the bundle (room+price) given to another tenant. Different papers have studied this problem under two incompatible assumptions: the miserly tenants assumption is that...
Given a finite set $X$ and an ordering $\succeq$ over its subsets, the $l$-out-of-$d$ maximin-share of $X$ is the maximal (by $\succeq$) subset of $X$ that can be constructed by partitioning $X$ into $d$ parts and picking the worst union of $l$ parts. A pair of integers $(l,d)$ dominates a pair $(l',d')$ if, for any set $X$ and ordering $\succeq$,...
We study the fair division of a continuous resource, such as a land-estate or a time-interval, among pre-specified groups of agents, such as families. Each family is given a piece of the resource and this piece is used simultaneously by all family members, while different members may have different value functions. Three ways to assess the fairness...
A set of objects is to be divided fairly among agents with different tastes, modeled by additive value functions. If the objects cannot be shared, so that each of them must be entirely allocated to a single agent, then fair division may not exist. How many objects must be shared between two or more agents in order to attain a fair division? The pap...
In two-sided markets, Myerson and Satterthwaite's impossibility theorem states that one can not maximize the gain-from-trade while also satisfying truthfulness, individual-rationality and no deficit. Attempts have been made to circumvent Myerson and Satterthwaite's result by attaining approximately-maximum gain-from-trade: the double-sided auctions...
We study monotonicity properties of solutions to the classic problem of fair cake-cutting—dividing a heterogeneous resource among agents with different preferences. Resource- and population-monotonicity relate to scenarios where the cake, or the number of participants who divide the cake, changes. It is required that the utility of all participants...
We study the problem of fairly allocating indivisible goods to groups of agents. Agents in the same group share the same set of goods even though they may have different preferences. Previous work has focused on unanimous fairness, in which all agents in each group must agree that their group's share is fair. Under this strict requirement, fair all...
A set of objects, some goods and some bads, is to be divided fairly among agents with different tastes, modeled by additive utility-functions. If the objects cannot be shared, so that each of them must be entirely allocated to a single agent, then fair division may not exist. What is the smallest number of objects that must be shared between two or...
We consider a multi-agent resource allocation setting that models the assignment of papers to reviewers. A recurring issue in allocation problems is the compatibility of welfare/efficiency and fairness. Given an oracle to find a welfare-achieving allocation, we embed such an oracle into a flexible algorithm called the Constrained Round Robin (CRR)...
Using a lab experiment, we investigate the real-life performance of envy-free and proportional cake-cutting procedures with respect to fairness and preference manipulation. We find that envy-free procedures, in particular Selfridge-Conway, are fairer and also are perceived as fairer than their proportional counterparts, despite the fact that agents...
Bipartite Envy-Free Matching (BEFM) is a relaxation of perfect matching. In a bipartite graph with parts X and Y, a BEFM is a matching of some vertices in X to some vertices in Y, such that each unmatched vertex in X is not adjacent to any matched vertex in Y (so the unmatched vertices do not "envy" the matched ones). The empty matching is always a...
An archipelago of $m$ islands has to be divided fairly among $n$ agents with different preferences. What fraction of the total archipelago value can be guaranteed to each agent? When each agent insists of getting a single connected piece (contained in a single island), the fraction is $1/(n+m-1)$. When each agent agrees to get up to m pieces, the f...
Fair division theory mostly involves individual consumption. But resources are often allocated to groups, such as families or countries, whose members consume the same bundle but have different preferences. Do fair and efficient allocations exist in such an "economy of families"? We adapt three common notions of fairness: fair-share, no-envy and eg...
Using a lab experiment, we investigate the real-life performance of envy-free and proportional cake-cutting procedures with respect to fairness and preference manipulation. We find that envy-free procedures, in particular Selfridge-Conway and the symmetric and asymmetric versions of cut-and-choose, are fairer and also are perceived as fairer than t...
A heterogeneous resource, such as a land-estate, is already divided among several agents in an unfair way.The challenge is to re-divide it among the agents in a way that balances fairness with ownership rights.We present re-division protocols that attain various combinations of fairness and ownership rights, in various settings differing in the geo...
We study the problem of fairly allocating indivisible goods to groups of agents. Agents in the same group share the same set of goods even though they may have different preferences. Previous work has focused on unanimous fairness, in which all agents in each group must agree that their group's share is fair. Under this strict requirement, fair all...
Motivated by applications such as stock exchanges and spectrum auctions, there is a growing interest in mechanisms for arranging trade in two-sided markets. However, existing mechanisms are either not truthful, do not guarantee an asymptotically-optimal gain-from-trade, rely on a prior on the traders' valuations, or operate in limited settings such...
A cake has to be divided fairly among $n$ agents. When all agents have equal entitlements, it is known that such a division can be implemented with $n-1$ cuts. When agents may have different entitlements, we show that at least $2 n -2$ cuts may be necessary, and $2 n\cdot \Theta(\log(n))$ cuts are always sufficient.
Level-1 consensus is a recently-introduced property of a preference-profile. Intuitively, it means that there exists a preference relation which induces an ordering of all other preferences such that frequent preferences are those that are more similar to it. This is a desirable property, since it enhances the stability of social choice by guarante...
In a seminal paper, McAfee (1992) presented a truthful mechanism for double auctions, attaining asymptotically-optimal gain-from-trade without any prior information on the valuations of the traders. McAfee's mechanism handles single-parametric agents, allowing each seller to sell a single unit and each buyer to buy a single unit. This paper present...
In a seminal paper, McAfee (1992) presented a truthful mechanism for double auctions, attaining asymptotically-optimal gain-from-trade without any prior information on the valuations of the traders. McAfee's mechanism handles single-parametric agents, allowing each seller to sell a single unit and each buyer to buy a single unit. This paper present...
A seminal theorem of Myerson and Satterthwaite (1983) proves that, in a game of bilateral trade between a single buyer and a single seller, no mechanism can be simultaneously individually-rational, budget-balanced, incentive-compatible and socially-efficient. However, the impossibility disappears if the price is fixed exogenously and the social-eff...
We study the problem of allocating indivisible goods to groups of interested agents in a fair manner. The agents in the same group share the same set of goods even though they may have different preferences from one another. Previous work on this model has shown positive results that hold either asymptotically or for groups with a small number of a...
Ranking alternatives is a natural way for humans to explain their preferences. It is being used in many settings, such as school choice (NY, Boston), course allocations, and the Israeli medical lottery. In some cases (such as the latter two), several "items" are given to each participant. Without having any information on the underlying cardinal ut...
Ranking alternatives is a natural way for humans to explain their preferences. It is being used in many settings, such as school choice, course allocations and residency matches. In some cases, several `items' are given to each participant. Without having any information on the underlying cardinal utilities, arguing about fairness of allocation req...
Recently (in arXiv preprint 1703.08150), Babaioff and Nisan and Talgam-Cohen introduced the following question. In a Fisher market with indivisible items, in which the agents' budgets are "generic" (do not satisfy a finite set of linear equalities), does there always exist a competitive equilibrium? For the setting in which agents can have arbitrar...
Level-1 consensus is a property of a preference profile. Intuitively, it means that there exists some preference relation such that, when ordering the other preference-relations by increasing distance from it, the closer preferences are more frequent in the profile. This is a desirable property, since it enhances the stability of the social choice...
There is a heterogeneous resource that contains both good parts and bad parts, for example, a cake with some parts burnt, or a land-estate with some parts polluted. The resource has to be divided fairly among n agents, each of whom has a personal value-density function on the resource. The value-density functions can accept any real value - positiv...
In the classic cake-cutting problem (Steinhaus, 1948), a heterogeneous resource has to be divided among n agents with different valuations in a proportional way --- giving each agent a piece with a value of at least 1/n of the total. In many applications, such as dividing a land-estate or a time-interval, it is also important that the pieces are co...
In the classic cake-cutting problem (Steinhaus, 1948), a heterogeneous resource has to be divided among n agents with different valuations in a proportional way --- giving each agent a piece with a value of at least 1/n of the total. In many applications, such as dividing a land-estate or a time-interval, it is also important that the pieces are co...
We consider the classic problem of fairly dividing a heterogeneous good (“cake”) among several agents with different valuations. Classic cake-cutting procedures either allocate each agent a collection of disconnected pieces, or assume that the cake is a one-dimensional interval. In practice, however, the two-dimensional shape of the allotted pieces...
In a large, possibly infinite population, each subject is colored red with probability $p$, independently of the others. Then, a finite sub-population is selected, possibly as a function of the coloring. The imbalance in the sub-population is defined as the difference between the number of reds in it and p times its size. This paper presents high-p...
We consider the classic problem of envy-free division of a heterogeneous good ("cake") among several agents. It is known that, when the allotted pieces must be connected, the problem cannot be solved by a finite algorithm for three or more agents. The impossibility result, however, assumes that the entire cake must be allocated. In this article, we...
In a seminal paper, McAfee (1992) presented the first dominant strategy truthful mechanism for double auction. His mechanism attains nearly optimal gain-from-trade when the market is sufficiently large. However, his mechanism may leave money on the table, since the price paid by the buyers may be higher than the price paid to the sellers. This mone...